Tum hume do thin question do solve karne ke liye

Answer: 1. Roots of $x^2 - 5x + 6 = 0$ are $x = 2, 3$ . 2. The $10^{\text{th}}$ term of the AP is $47$ . 3. The midpoint is $(4, 6)$ .

Step-by-step solution

Step 1: Solve Question 1: Quadratic Equation

To solve $x^2 - 5x + 6 = 0$ , factorize the quadratic expression by finding two numbers whose sum is $-5$ and product is $6$ . These numbers are $-2$ and $-3$ . Setting each factor to $0$ gives the roots $x = 2$ and $x = 3$ .

Step 2: Solve Question 2: Finding the nth Term of an AP

For the arithmetic progression $2, 7, 12, \dots$ , the first term is $a = 2$ and the common difference is $d = 7 - 2 = 5$ . Using the standard formula $a_n = a + (n - 1)d$ with $n = 10$ , we obtain $a_{10} = 47$ .

Step 3: Solve Question 3: Midpoint Formula

To find the midpoint between $(2, 4)$ and $(6, 8)$ , take the average of the $x$ -coordinates and the $y$ -coordinates. This evaluates to $(4, 6)$ .

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