Question

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

Answer 1

We have been given that,

We have to find a and b

Now, if is a root of the equation, then it should satisfy the equation completely. Therefore we substitute in the above equation. We get,

…… (1)

Also, if is a root of the equation, then it should satisfy the equation completely. Therefore we substitute in the above equation. We get,

…… (2)

Now, we multiply equation (2) by 9 and then subtract equation (1) from it. So we have,

Now, put this value of ‘a’ in equation (2) in order to get the value of ‘b’. So,

Therefore, we have and .