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Question
If 'p' is a root of the quadratic equation x2 – (p + q) x + k = 0, then the value of 'k' is ______.
Options
p
q
p + q
pq
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Solution
If 'p' is a root of the quadratic equation x2 – (p + q) x + k = 0, then the value of 'k' is pq.
Explanation:
Let the roots of given quadratic equation be α and β.
On comparing equation x2 – (p + q) x + k = 0
with ax2 + bx + c = 0, we have
a = 1, b = –(p + q), c = k
We know that
`\implies` α + β = `(-b)/a`
Put the value a and b
`\implies` α + β = `(p + q)/1`
`\implies` α + β = p + q ...(1)
Given α = p
Put the value of α in equation (1),
`\implies` p + β = p + q
`\implies` β = q
But we know that
α.β = `c/a`
Put the values
p.q. = `k/1`
Then, k = pq.
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