If x = 2/3 and x = -3 are the roots of the quadratic equation ax2 + 7

1.	If x = 2/3 and x = -3 are the roots of the quadratic equation ax2 + 7x + b = 0 then find the values of a and b.
Answer» Given roots are: x = 2/3 and x = -3 and quadratic equation ax² + 7x + b = 0 Since x = 2/3 and x = -3 are roots of the above quadratic equation Hence, will satisfy the given equation. Step 1: At x = 2/3 a(2/3)² + 7(2/3) + b=0 4/9 a + 14/3 + b = 0 4a + 42 + 9b = 0 ………….equation (1) Step 2: At x = –3 a(-3)²+ 7(-3)+b=0 9a – 21 + b = 0 ………….equation (2) Step 3: Solving equation (1) and equation (2), we get a = 3, b = –6

If x = 2/3 and x = -3 are the roots of the quadratic equation ax2 + 7x + b = 0 then find the values of a and b.

Answer»

Given roots are: x = 2/3 and x = -3

and quadratic equation ax² + 7x + b = 0

Since x = 2/3 and x = -3 are roots of the above quadratic equation

Hence, will satisfy the given equation.

Step 1: At x = 2/3

a(2/3)² + 7(2/3) + b=0

4/9 a + 14/3 + b = 0

4a + 42 + 9b = 0 ………….equation (1)

Step 2: At x = –3

a(-3)²+ 7(-3)+b=0

9a – 21 + b = 0 ………….equation (2)

Step 3: Solving equation (1) and equation (2), we get

a = 3, b = –6