Question

Quadratic polynomial 2x²-3x+1 has zeroes as α and β.Form a quadratic polynomial whose zeroes are 3α and 3β​

Answer 1

Case 1 :-

For quadratic equation $2x-3x+1=0$, zeros are $\alpha$ and $\beta$.

$\alpha +\beta =\frac{-b}{a} =\frac{-3}{2}$

$\alpha \beta =\frac{c}{a} =\frac{1}{2}$

Case 2 :-

For some quadratic equation , zeros are $3\alpha$ and $3\beta$.

$3\alpha +3\beta =3*\frac{-b}{a} =3*\frac{-3}{2}=\frac{-9}{2}$

$3*3\alpha \beta =9*\frac{c}{a} =9*\frac{1}{2}=\frac{9}{2}$

So from the above,

$a=2$

$b= -9$

$c=9$

   $ax^2+bx+c=0$

⇒ $2x^2-9x+9=0$