QJEEM18Ma2ec5: JEE Main 2018 Mathematics - Class 11 JEEM18Ma2ec5 Solution: If f(x) is a quadratic expression such that f (1) + f (2) = 0,…

Question

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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 :

Accepted Answer

Let

α

and

β

= - 1 are the roots of the polynomial, then we get

f(x) = x² + (1 -

α

)x -

α

∴

f(1) = 2 - 2

α

and f(2) = 6 - 3

α

Also given,

f (1) + f (2) = 0

∴

2 - 2

α

+ 6 - 3

α

= 0

\Rightarrow

α

=

\frac{8}{5}

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