Question

Find the value of p so that the equations 3x 2-6x+3p=0 has equal roots . Also find the roots

Answer 1

the value of p is 1 and the roots are 1,1

Answer 2

$3 {x}^{2} - 6x + 3p = 0$
let both root are
$\alpha$
apply the formula of addition of roots and Multiplication of roots,with the cofficient of equation
$\alpha + \alpha = \frac{ - b}{a} = \frac{6}{3} = 2$
${ \alpha }^{2} = \frac{c}{a} = \frac{3p}{3} = p$
$2 \alpha = 2 \\ \alpha = 1$
${ \alpha }^{2} = p \\ 1 = p$
so the value of p=1.
by factorisation of polynomial by putting the value of p.
the roots are 1,1