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# Find the roots of each of the following equations, if they exist, by applying the quadratic formula:x2 + 5x – (a2 + a – 6) = 0

Given: x2 + 5x – (a2 + a – 6) = 0

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

A = 1, B = 5, C = – (a2 + a – 6)

Discriminant D = B2 – 4AC

= (5)2 – 4.1. – (a2 + a – 6)

= 25+ 4a2 + 4a – 24 = 4a2 + 4a + 1

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

Hence the roots of equation are real. = (2a + 1)

Roots are given by  x = (a – 2) or x = – (a + 3)

Hence the roots of equation are (a – 2) or x = – (a + 3)

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