Question

If $\alpha$ and $\beta$ are the zeros of the quadratic polynomial $x^2-3x+2$, then a quadratic polynomial whose zeros are $\frac{1}{2\alpha +\beta }$ and $\frac{1}{2\beta +\alpha }$ is?

• A. $20x^2+9x+1$
• B. $20x^2-9x-1$
• C. $20x^2-9x+1$
• D. $20x^2+9x-1$

Answer 1

The correct option is C $20x^2-9x+1$

given $X^2-3X+2$ sum of the roots is $\alpha +\beta$ is $-b/a$ that is $3$ and product of the roots $\alpha \ast \beta$ is $c/a$ that is $2$ so using the same values for the question also.

as the roots given are $1/(2\alpha +\beta )$ and $1/(2\beta +\alpha )$ so sum of roots on solving is $3(\alpha +\beta )/\left(2\right((\alpha +\beta {)}^2)(\alpha \ast \beta ))=(9/20)$ product of the roots is $1/\left(2\right((\alpha +\beta {)}^2)+(\alpha \ast \beta )\left)is\right(1/20)$

hence on matching same option C is correct.