# Find the roots of each of the following equations, if they exist, by applying the quadratic formula:x2 + 6x – (a2 + b2 – 8) = 0

Given: x2 + 6x – (a2 + b2 – 8) = 0

Comparing with standard quadratic equation Ax2 + Bx + C = 0

A = 1, B = 6, C = – (a2 + b2 – 8)

Discriminant D = B2 – 4AC

= (6)2 – 4.1. – (a2 + b2 – 8)

= 36+ 4a2 + 8a – 32 = 4a2 + 8a + 4

= 4(a2 + 2a + 1)

= 4(a + 1)2 > 0 Using a2 + 2ab + b2 = (a + b)2

Hence the roots of equation are real.

= 2(a + 1)

Roots are given by

x = (a – 2) or x = – (4 + a)

Hence the roots of equation are (a – 2) or – (4 + a)

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