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

To Find: a and b

Concept Used:

If k is a root of a polynomial f(x), then f(k) = 0

Explanation:

Let f(x) = ax² + 7x + b = 0

Now,

4a + 42 + 9b = 0

4a + 9b = –42 …..(1)

f(–3) = = a(–3)² + 7(–3) + b = 0

9a + b – 21 = 0

9a + b = 21….(2)

Multiplying equation (2) by 9, we get,

81a + 9b = 189….(3)

Subtracting equation (1) from equation (3), we get,

81a – 4a + 9b – 9b = 189 – (–42)

77a = 231

a = 3

Putting the value of a in equation 1, we get,

4 × 3 + 9b = –42

12 + 9b = –42

9b = –54

b = –6