Polynomials — Class 10 solved problems

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

1. Find k if the sum of the zeroes of x² - (k + 6)x + 2(2k + 1) is half of their product.

   The value of k is 5.

2. Find the zeroes of the polynomial p(x) = x² - 5x + 6 and verify the relationship between the zeroes and the coefficients.

   The zeroes of the polynomial p(x) = x² - 5x + 6 are x=2 and x=3. The relationship between the zeroes and coefficients is verified as: Sum of zeroes = 2+3=5 and

3. While playing in a garden, Samaira saw a honeycomb and asked her mother about it. Her mother replied that it is a honeycomb. Also, she told her that the shape o

   (i) There are 3 zeroes. (ii) The zeroes are -2, 1, and 3. (iii) (a) a = -6, b = 6. (iii) (b) p = ± 18.

4. If α, β are the zeroes of the polynomial 3x² - 13x - 10, then find the value of (3α + 1)(3β + 1).

   -16

5. Assertion (A) If the graph of a polynomial intersects the x-axis at exactly two points, then the number of zeroes of that polynomial is 2. Reason (R) The number

   Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).

6. The zeroes of the polynomial 3x² + 11x - 4 are:

   The zeroes of the polynomial are (1)/(3) and -4.

7. Verify that 3, -1, -(1)/(3) are the zeroes of the cubic polynomial p(x) = 3x³ - 5x² - 11x - 3, and then verify the relationship between the zeroes and the coeff

   The values 3, -1, -(1)/(3) are verified to be the zeroes of the polynomial p(x) = 3x³ - 5x² - 11x - 3. The relationships between the zeroes and the coefficients

8. If the product of the zeroes of the quadratic polynomial 5x² + 7x + k is - (2)/(5), then the value of k is:

   The value of k is -2.

9. Find the zeroes of the polynomial x² - 3 and verify the relationship between the zeroes and the coefficients.

   The zeroes of the polynomial x² - 3 are √3 and -√3. Verification: Sum of zeroes: √3 + (-√3) = 0. -b/a = -0/1 = 0. (Verified) Product of zeroes: (√3)(-√3) = -3.

10. Look at the graphs in Fig. 2.9 given below. Each is the graph of y = p(x), where p(x) is a polynomial. For each of the graphs, find the number of zeroes of p(x)

    (i) 1, (ii) 2, (iii) 3, (iv) 1, (v) 1, (vi) 4

11. Find a quadratic polynomial, the sum and product of whose zeroes are -3 and 2, respectively.

    The quadratic polynomial is x² + 3x + 2.

12. Find the zeroes of the quadratic polynomial x² + 7x + 10, and verify the relationship between the zeroes and the coefficients.

    The zeroes of the quadratic polynomial x² + 7x + 10 are -2 and -5. The relationship between the zeroes and coefficients is verified as the sum of zeroes (-2 + (

13. The zeroes of the polynomial x² + 5x + 6 are:

    The zeroes of the polynomial x² + 5x + 6 are -2 and -3.

14. Find the zeroes of the quadratic polynomial x² - 2x - 8 and verify the relationship between the zeroes and the coefficients.

    The zeroes of the quadratic polynomial x² - 2x - 8 are 4 and -2. The relationships between the zeroes and coefficients are verified as: Sum of zeroes (4 + (-2)

More Class 10 chapters

• Real Numbers26 solved
• Pair of Linear Equations in Two Variables37 solved
• Quadratic Equations49 solved
• Arithmetic Progressions38 solved
• Triangles33 solved
• Coordinate Geometry44 solved
• Introduction to Trigonometry37 solved
• Some Applications of Trigonometry32 solved
• Circles32 solved
• Areas Related to Circles42 solved
• Surface Areas and Volumes17 solved
• Statistics18 solved
• Probability22 solved

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