Mathematics
If the roots of the quadratic equation, px(x - 2) + 6 = 0 are equal, then the value of p is:
0
4
6
none of these
Quadratic Equations
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Answer
Given,
⇒ px(x - 2) + 6 = 0
⇒ px2 - 2px + 6 = 0
Comparing px2 - 2px + 6 = 0 with ax2 + bx + c = 0 we get,
a = p, b = -2p and c = 6.
We know that,
Since equations has equal roots,
⇒ D = 0
⇒ b2 - 4ac = 0
⇒ (-2p)2 - 4(p)(6) = 0
⇒ 4p2 - 24p = 0
⇒ 4p(p - 6) = 0
⇒ 4p = 0 or p - 6 = 0 [Using Zero-product rule]
⇒ p = 0 or p = 6.
Since p = 0 would make the equation no longer quadratic, we take:
p = 6
Hence, option 3 is the correct option.
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