Mathematics
Find the value of 'p', if the following quadratic equation has equal roots :
4x2 - (p - 2)x + 1
Quadratic Equations
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Answer
Comparing 4x2 - (p - 2)x + 1 = 0 with ax2 + bx + c = 0 we get,
a = 4, b = -(p - 2) and c = 1.
Since equations have equal roots,
∴ D = 0
⇒ (-(p - 2))2 - 4.(4).(1) = 0
⇒ (p2 + 4 - 4p) - 16 = 0
⇒ p2 - 4p - 12 = 0
⇒ p2 - 6p + 2p - 12 = 0
⇒ p(p - 6) + 2(p - 6) = 0
⇒ (p + 2)(p - 6) = 0
⇒ (p + 2) = 0 or (p - 6) = 0
⇒ p = -2 or p = 6.
Hence, p = -2 or p = 6.
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