Mathematics
Find the value of 'p', if the following quadratic equation has equal roots :
x2 + (p - 3)x + p = 0
Quadratic Equations
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Answer
Comparing x2 + (p - 3)x + p = 0 with ax2 + bx + c = 0 we get,
a = 1, b = (p - 3) and c = p.
Since equations have equal roots,
∴ D = 0
⇒ (p - 3)2 - 4.(1).(p) = 0
⇒ (p2 + 9 - 6p) - 4p = 0
⇒ p2 - 10p + 9 = 0
⇒ p2 - 9p - p + 9 = 0
⇒ p(p - 9) - 1(p - 9) = 0
⇒ (p - 1)(p - 9) = 0
⇒ (p - 1) = 0 or (p - 9) = 0
⇒ p = 1 or p = 9.
Hence, p = 1 or p = 9.
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