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 :
JEE · Math · previous-year question
- A.$$-$$ $${5 \over 8}$$
- B.$$-$$ $${8 \over 5}$$
- C.$${5 \over 8}$$
- D.$${8 \over 5}$$correct
Answer
D. $${8 \over 5}$$
Explanation
Let $$\alpha $$ and $$\beta $$ = - 1 are the roots of the polynomial, then we get f(x) = x2 + (1 - $$\alpha $$)x - $$\alpha $$ $$ \therefore $$ f(1) = 2 - 2$$\alpha $$ and f(2) = 6 - 3$$\alpha $$ Also given, f (1) + f (2) = 0 $$ \therefore $$ 2 - 2$$\alpha $$ + 6 - 3$$\alpha $$ = 0 $$ \Rightarrow $$ $$\alpha $$ = $${8 \over 5}$$
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