Q. 174.8( 13 Votes )

Find the value of a for which the equation (a – 12)x2 + 2(a – 12)x + 2 = 0 has equal roots.

Answer :

Given that the quadratic equation (a – 12)x2 + 2(a – 12)x + 2 = 0 has equal roots

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


A = (a – 12) B = 2(a – 12) C = 2


Thus D = 0


Discriminant D = B2 – 4AC≥0


[2(a – 12)]2 – 4(a – 12)2≥0


4(a2 + 144 – 24a) – 8a + 96 = 0 using (a – b)2 = a2 – 2ab + b2


4a2 + 576 – 96a – 8a + 96 = 0


4a2 – 104a + 672 = 0


a2 – 26a + 168 = 0


a2 – 14a – 12a + 168 = 0


a(a – 14) – 12(a – 14) = 0


(a – 14)(a – 12) = 0


a = 14 or a = 12


for a = 12 the equation will become non quadratic – – (a – 12)x2 + 2(a – 12)x + 2 = 0


A, B will become zero


Thus value of a = 14 for which the equation has equal roots.


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