Question

If ∝,β are the roots of the equation 2$x^2$ - 3x - 5 = 0, then the equation whose roots are $\frac{5}{\propto }$ , $\frac{5}{\beta }$ is :

• A. x² - 3x - 10 = 0
• B. x² + 3x - 10 = 0
• C. x² + 3x + 10 = 0
• D. x² - 3x + 10 = 0

Answer 1

The correct option is B

x² + 3x - 10 = 0

2$x^2$ -3x -5 =0

Therefore α+β= $\frac{3}{2}$ , αβ=$\frac{-5}{2}$

λ1=$\frac{5}{\alpha }$+$\frac{5}{\beta }$ = 5$\frac{(\alpha +\beta )}{\alpha \beta }$ =-3

and λ2=$\frac{25}{\alpha \beta }$=-10

$x^2$ + 3x - 10 = 0