Question

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

Answer 1

♦GOOD MORNING ♦

Given Quadratic Equation is

ax² + 7x + b = 0

For x = 2/3 we have

a(2/3)² + 7(2/3) + b = 0

4a + 42 + 9b = 0

4a + 9b = -42 ... Equation i

For x = -3 we have

a(-3)² + 7(-3) + b = 0

9a - 21 + b = 0

9a + b = 21 ... Equation ii

Multiply Equation i by 9 and ii by 4 we have

36a + 81b = -378 ... Equation iii

36a + 4b = 84 ... Equation iv

Subtract Both The Equations we have

81b - 4b = -378 - 84

77b = -462

b = 6

Now, substitute value of b in Equation ii we have:)

9a + 6 = 21

9a = 21 - 6

9a = 15

a = 5/3

Therefore, a = 5/3 And b = 6