Question

if x=2/3 and x=-3 are the roots of the QE ax^2+7x+b=0find value of A and b

Answer 1

Given that x = 2/3 and x = -3 are the roots of the equation


=> x - 2/3 = 0 and x + 3 = 0 are the factors of the given polynomial ax² + 7x + b

Now,

x - 2/3 = 0

Multiply 3 on both sides

=> 3(x - 2/3) = 3(0)

=> 3x - 2 = 0

So 3x - 2 and x + 3 are the two factors of the given quadratic equation. Since a quadratic equation has only two factors, it means that when we will multiply the factors, the product will be the polynomial.

=> (3x - 2)(x + 3) = ax² + 7x + b

=> 3x² + 9x - 2x - 6 = ax² + 7x + b

=> 3x² + 7x - 6 = ax² + 7x + b


Now if we will compare them, then :-

In LHS, coefficient of x² is 3 and in RHS coefficient of x² is a

=> a = 3

Similarly, in LHS the constant term is - 6 and in RHs the constant term is b

=> b = -6

So your answer,

a = 3

b = - 6


Hope it helps dear friend ☺️✌️