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Question

If x2ax+b=0 and x2px+q=0 have one root common and the second equation has equal roots, then b+q is equal to


A
p+a
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B
p2
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C
ap2
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D
a2
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Solution

The correct option is C ap2
Let the root of x2px+q=0 be β
2β=p, β2=q
β=p2=±q     (1)

Now for x2ax+b=0,
let the roots be α and β.
α+β=a, αβ=b
From (1),
α=2ap2,  2ap2p2=b

p2(2ap)2=b
4b=2app2
4b+p2=2ap
4b+4q=2ap    [p2=±q]
b+p=ap2

Mathematics

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