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Question

If one root of the quation ax2+bx+c=0 is double the other, then the relation between a,b,c, is

A
2b2=9ac
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B
b2=ac
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C
b2=3ac
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D
b2=9ac
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Solution

The correct option is A 2b2=9ac
If the roots of the equation ax2+bx+c=0 are α and β
Then α+β=ba ....(1)
and αβ=ca .....(2)
Let β=2α
Using (1) and (2), we have
α+2α=ba
α=b3a .....(3)
and 2α2=ca .....(4)
Substituting (3) in (4), we get
2(b3a)2=ca

2b2=9ca

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