If f(x) is a quadratic expression such that f(1)+f(2)=0, and −1 is a root of f(x)=0. Find the other root of f(x)=0.

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- \frac{5}{8}

- \frac{8}{5}

\frac{5}{8}

\frac{8}{5}

answer is D.

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Detailed Solution

Let’s first try to analyse the question properly. Here we have a quadratic polynomial f(x) which satisfies the equation f(1)+f(2)=0 and it has a root −1 . With this information, we need to find the other root for f(x)=0
As we know that, the general form of a quadratic equation is

{ax}^{2} + bx + c = 0

and the part on the left side is called the general form of a quadratic expression. And the quadratic expression in variable x and with roots as α and β can be written as (x−α)(x−β)
Therefore, let’s assume f(x)=(x−α)(x−β)=

x^{2}

−(α+β)x+αβ
But it is already given that the equation f(x)=0 has a root −1
Hence, we can write the function as f(x)=(x+1)(x−β)=

x^{2}

−(−1+β)x+(−1)β=

x^{2}

−(β−1)x−β
According to the question, the given function satisfies: f(1)+f(2)= 0
We can substitute the expression for f(1) and f(2) into the above equation to solve for β
⇒f(1)+f(2) = 0
⇒(