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Question

If the roots of ax2bxc=0 are increased by same quantity then which of the following expression does not change?

A
b24aca2
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B
b24aca
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C
b2+4aca2
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D
b2+4aca
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Solution

The correct option is C b2+4aca2
Let the roots of the equation ax2bxc=0 be α,β
Assuming that the roots are increased by k, so new roots are α+k,β+k.
By observation we can see that differenece of roots αβ remains same.
So,
(αβ)2=(α+β)24αβ =b2a24(ca) =b2+4aca2

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