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Question

Find the quadratic equation whose roots exceeds the roots of quadratic equation x22x+3=0 by 2

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Solution

Given that,
x22x+3=0
Let the roots be α,β
Let the roots of the other quadratic equation be A,B.
Given that the roots of the other quadratic equation exceeds the roots of the given equation by 2.
A=α+2 and B=β+2

Now, we know that,
Sum of roots=ba
and Product of roots=ca

Hence, α+β=2
and αβ=3

Now, A+B=(α+2)+(β+2)=α+β+4=6
and, AB=(α+2)(β+2)=αβ+2(α+β)+4=3+4+4=11

Hence, A+B=6 and AB=11

Now, the quadratic equation having roots A and B is:
x2(A+B)x+AB=0
Substituting the values of A+B and AB in the equation, we get:
x26x+11=0

Hence, the required quadratic equation is x26x+11=0.

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