If f(x) is a quadratic expression such that f(1)+f(2)=0, and −1 is a root of f(x)=0 then the other root of f(x)=0 is:
A
−58
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B
−85
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C
58
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D
85
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Solution
The correct option is D85 Let the quadratic equation is f(x)=x2+bax+ca As, −1 and β are the roots of quadratic equation ∴−1+β=−ba⇒ba=1−β and (−1)β=ca⇒ca=−β So, f(x)=x2+(1−β)x−β Now, f(1)+f(2)=0 ⇒(1+(1−β)−β)+(4+(1−β)2−β)=0 ⇒β=85