Question

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

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

Answer 1

The correct option is A $x^2-4x+4=0$

Given $\alpha ,\beta$ are the roots of equation $x^2-3x+5=0$
So,
${\alpha }^2-3\alpha +5=0{\beta }^2-3\beta +5=0$
$\therefore {\alpha }^2-3\alpha =-5\text{and}{\beta }^2-3\beta =-5$
Now,
${\alpha }^2-3\alpha +7=2\text{and}{\beta }^2-3\beta +7=2$

Hence, the quadratic equation whose roots are $2,2$ is
$(x-2{)}^2=0\therefore x^2-4x+4=0$