Quadratic Equations — Class 10 solved problems

49 problems from this chapter, each solved step by step.

Two couriers, Jack and Jill, start walking at the same instant from two towns, A and B, heading towards each other at constant speeds.They pass each other at a
Jack's speed is 16 km/h, Jill's speed is 12 km/h, and the total distance between town A and town B is 336 km.
Find all integer values of n for which the expression (7n-12)/(2n+3) results in a perfect square.
n = 3 and n = -24
Can you solve Xpower3+28x-14x=0
Real solution: x = 0 (or complex solutions: x = 0, ± i√14)
Find the roots of the quadratic equation 6x² - 23x + 21 = 0 by factorisation.
The roots of the quadratic equation are x = (3)/(2) and x = (7)/(3).
Solve for x in terms of a and b: (1)/(a+b+x)=(1)/(a)+(1)/(b)+(1)/(x)(Where a, b, x ≠ 0 and a + b + x ≠ 0)
x = -a or x = -b
Solve for x: 2x² - 7x + 3 = 0. I am a class 10 student, please help me understand how to do it.
The solutions for x are 3 and (1)/(2).
A ball is thrown upward from the top of a 20-meter-high building. Its height h h in meters after t t seconds is given by: h ( t) = − 5 t 2 + 15 t + 20 h(t)=−5t
The ball hits the ground after 4 seconds.
If the roots of x² + px + q = 0 are in the ratio 2:3, prove that 6p² = 25q.
The proof shows that if the roots of x² + px + q = 0 are in the ratio 2:3, then 6p² = 25q.
Solve the quadratic equation 3x² - 5x + 2 = 0 using the quadratic formula x = (-b ± √(b² - 4ac))/(2a).
The solutions to the quadratic equation 3x² - 5x + 2 = 0 are x = 1 and x = (2)/(3).
A line y = c reflects the quadratic y = x² - 4x + 7 to yield y = -x² + 4x + 1. Find c and the vertex of the new parabola.
The value of c is 4 and the vertex of the new parabola is (2, 5).
Solve for x in the exponential equation: 2²x - 9 · 2^x + 8 = 0
The solutions for x are 0 and 3.
Find the roots of the quadratic equation 2x² - 7x + 3 = 0 using the quadratic formula, and state the value of the discriminant.
The roots of the quadratic equation are x = 3 and x = (1)/(2). The discriminant is 25.
Q1: Check whether the following are quadratic equations: (i) (x+1)² = 2(x-3) Sol: x²+1+2x = 2x-6 x²+1+2x-2x-6=0 x²+7=0 It is in the form of ax²+bx+c=0. Hence th
Both given equations are quadratic equations.
Solve using the quadratic formula: 2x² + 5x − 3 = 0.
The solutions are x = (1)/(2) and x = -3.
Quadratic Equation Any equation is in the form of ax² + bx + c = 0 where a ≠ 0 is a quadratic equation. Q1: Check whether the following are quadratic equations:
Yes, the given equation (x+1)² = 2(x-3) is a quadratic equation.
Find the roots of the equation 2x² - 5x + 3 = 0 by factorisation.
The roots of the equation are x = 1 and x = (3)/(2).
Solve the quadratic equation x² - 5x + 6 = 0
The solutions to the quadratic equation x² - 5x + 6 = 0 are x=3 and x=2.
Solve the quadratic equation 2x² - 7x + 3 = 0 using the quadratic formula.
The solutions are x = 3 and x = (1)/(2).
(a) If Nidhi were 7 years younger than what she actually is, then the square of her age (in years) would be 1 more than 5 times her actual age. What is her pres
The shopkeeper bought 30 books initially.
If x = 5 is a solution of the quadratic equation 2x² + (k - 1)x + 10 = 0, then the value of k is
k = -11
A man in a boat goes 12 km downstream and comes back to the starting point by rowing non-stop in a total time of 3 hours. If the speed of the stream is 3 km/h,
The speed with which the man can row the boat in still water is 9 km/h.
Two water taps together can fill a tank in 3(3)/(13) hours. The tap of larger diameter takes 5 hours less than the smaller one to fill the tank separately. Find
The smaller tap takes approximately 9.81 hours and the larger tap takes approximately 4.81 hours to fill the tank separately.
The values of k for which the equation 4x² + kx + 9 = 0 has real and equal roots are:
k = ± 12
Ashok and Harish are very close friends. They decided to go on a long drive with their families in separate cars. Ashok's car travels at a speed of x km/h, whil
(i) The distance covered by Harish's car in two hours is 2(x+5) km. (ii) The quadratic equation describing the speed of Ashok's car is x² + 5x - 500 = 0. (iii)
What What is What is What is x What is x square What is x square What is x square minus What is x square minus What is x square minus What is x square minus Wha
The equation x² - 3x - y = 0 represents a parabola.
Question: The sum of the ages of a father and his son is 45 years. Five years ago, the product of their ages was 124. Find their present ages.
The present age of the father is 36 years and the present age of the son is 9 years.
X square + 2 X + 3 is equal to zero
The equation has no real roots.
Find the roots of the equation (1)/(2x-3) + (1)/(x-5) = 1 x ≠ (3)/(2), 5 (rational equation, roots, domain, excluded values)
The roots of the equation are x = (8 + 3√2)/(2) and x = (8 - 3√2)/(2).
Find the roots of the equation (1)/(2x-3) + (1)/(x-5) = 1 x ≠ (3)/(2), 5 (roots, equation, fractions, domain, quadratic)
The roots of the equation are x = (8 + 3√2)/(2) and x = (8 - 3√2)/(2).
Which one of the following equations does not have real roots?
The equation x² - 4x + 3√2 = 0 does not have real roots.
Sketch the graph of y = x² - 4 and find its roots.
The roots of the equation y = x² - 4 are x = 2 and x = -2. The graph is a parabola opening upwards with its vertex at (0, -4), intersecting the x -axis at (2, 0
Find the roots of the quadratic equation x² + 7x + 10 = 0 by factorisation.
The roots of the quadratic equation are x = -2 and x = -5.
If the equation a(b - c)x² + b(c - a)x + c(a - b) = 0 has equal roots, where a + c = 15 and b = (36)/(5), then a² + c² is equal to
a² + c² = 144.4
Solve the quadratic equation using factorization: x² - 5x + 6 = 0.
The solutions are x = 2 and x = 3.
Find the roots of the quadratic equation 2x² - 5x + 3 = 0, by factorisation.
The roots of the equation 2x² - 5x + 3 = 0 are x = 1 and x = (3)/(2).
VARIATION: Find all real solutions to the equation: √(variable_93 + 3 - 4√(variable_93 - 1)) + √(variable_93 + 8 - 6√(variable_93 - 1)) = 1. Find the numerical
The real solutions are x [5, 10].
Find the discriminant of the quadratic equation 2x² - 4x + 3 = 0, and hence find the nature of its roots.
The discriminant is -8. Since the discriminant is less than 0, the quadratic equation has no real roots.
Consider the equation x² + 4x - n = 0 where n [20,100] is a natural number. Then the number of all distinct values of n, for which the given equation has integr
6
Find all values of k for which the equation (k-2)x² - 2(k-1)x + k = 0 has equal roots.
The only value of k for which the equation has equal roots is k=2.
Find the dimensions of the prayer hall discussed in Section 4.1. (The breadth x satisfies 2x² + x - 300 = 0.)
The breadth of the prayer hall is 12 m and the length is 25 m.
Product of two consecutive positive integers is 306. Find them.
The two consecutive positive integers are 17 and 18.
In a flight of 600 km, an aircraft was slowed due to bad weather. Its average speed for the trip was reduced to 200 km/hr and time of flight increased by 30 min
The original duration of flight was 1 hour.
EXTENSION: Find all values of k for which the equation (k-2)variable_95² - 2(k-1)variable_95 + k = 0 has equal roots. Additionally, generalize your solution to
There are no values of k for which the given quadratic equation has equal roots in the standard sense. However, if k=2, the equation becomes linear with a singl
Solve the quadratic equation: 2x² - 7x + 3 = 0
The solutions are x = 3 and x = (1)/(2).
Find the roots of 2x² - 5x + 3 = 0 by factorisation.
The roots of the equation 2x² - 5x + 3 = 0 are x = (3)/(2) and x = 1.
Find the roots of the quadratic equation: 3x² - 5x + 2 = 0 using the quadratic formula.
The roots of the quadratic equation 3x² - 5x + 2 = 0 are x = 1 and x = (2)/(3).
Find the roots of the quadratic equation 3x² - 2√6x + 2 = 0.
The roots of the equation are x = (√6)/(3) and x = (√6)/(3).
A pole has to be erected at a point on the boundary of a circular park of diameter 13 metres in such a way that the differences of its distances from two diamet
Yes, it is possible to erect the pole. The pole should be erected at a distance of 5 m from gate B and 12 m from gate A.
Let the equation x(x+2)(12-k)=2 have equal roots. Then the distance of the point (k,(k)/(2)) from the line 3x+4y+5=0 is:
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