Question

If $\alpha$ and $\beta$ are the zeroes of the quadratic polynomial $f\left(x\right)=x^2-2x+1$, then find a quadratic polynomial whose zeroes are $\frac{2\alpha }{\beta }$ and $\frac{2\beta }{\alpha }$

• A. k(x² - 4x + 4)
• B. k (8x² + 3x + 5)
• C. k (4x² - 9x - 1)
• D. k (3x² + x + 7)

Answer 1

The correct option is A

k(x² - 4x + 4)

$f\left(x\right)=x^2-2x+1$
Zeros of f(x) are $\alpha$ and $\beta$
Sum of zeroes = $\alpha +\beta =2$ and
Product of zeroes = $\alpha .\beta =1$
$\frac{2\alpha }{\beta }+\frac{2\beta }{\alpha }=2(\frac{\alpha }{\beta }+\frac{\beta }{\alpha })$
Required polynomial =$k(x^2-4x+4)$, where k is any integer.