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Question
The roots of the quadratic equation px2 – qx + r = 0 are real and equal if ______.
Options
p2 = 4qr
q2 = 4pr
– q2 = 4pr
p2 > 4pr
Solution
The roots of the quadratic equation px2 – qx + r = 0 are real and equal if q2 = 4pr.
Explanation:
Given, equation is px2 – qx + r = 0
On comparing it with ax2 + bx + c = 0, we get
a = p, b = – q, c = r
For roots to be equal, D = 0
i.e., b2 – 4ac = 0
`\implies` (– q)2 – 4 × p × r = 0
`\implies` q2 – 4pr = 0
`\implies` q2 = 4pr
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