Q7 of 39 Page 91

Find the values of p for which the following quadratic equation has two equal roots:

(p – 12)x2 + 2(p – 12)x + 2 = 0.

For roots to be equal, determinant must be equal to 0.

in case of quadratic eq., ax2 + bx + c = 0


determinant (D) = b2 – 4ac


According to the question, ; a = p – 12


b = 2(p – 12)


c = 2


So, 4(p – 12)2 – 4(p – 12)*2 = D


⇒ 4(p2 + 144 – 24p) – 8(p – 12) = 0


⇒ 4p2 + 576 – 96p – 8p + 96 = 0


⇒ 4p2 – 104p + 672 = 0


⇒ p2 – 26p + 168 = 0


⇒ p2 – 12p – 14p + 168 = 0


⇒ p(p – 12) – 14(p – 12) = 0


⇒ (p – 12)(p – 14) = 0


⇒ p = 12 or p = 14


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