Question

If $\alpha ,\beta$ are the root of a quadratic equation $x^2-3x+5=0$, then the equation whose roots are $({\alpha }^2-3\alpha +7)$ and $({\beta }^2-3\beta +7)$ is

• A. $x^2+4x+1=0$
• B. $x^2-4x+4=0$
• C. $x^2-4x-1=0$
• D. $x^2+2x+3=0$

Answer 1

Answer: (B)

$x^2-4x+4=0$

Since $\alpha ,\beta$ are the root of equation $x^2-3x+5=0$
So, ${\alpha }^2-3\alpha +5=0$
${\beta }^2-3\beta +5=0$
$\therefore {\alpha }^2-3\alpha =-5$
${\beta }^2-3\beta =-5$
Putting in $({\alpha }^2-3\alpha +7)$ & $({\beta }^2-3\beta +7)$ ....... (1)
$-5+7,-5+7$
$\therefore$ 2 and 2 are the roots
$\therefore$ The required equation is $x^2-4x+4=0$