Question

If the equations $a{x}^2+bx+c=0$ and $x^3+3x^2+3x+2=0$ have two common roots, then

• A. $a=2b=c$
• B. $a=b=c$
• C. $b^2=4ac$
• D. None of these

Answer 1

The correct option is B $a=b=c$

$a{x}^2+bx+c=0$

$\alpha +\beta =-\frac{b}{a},\alpha \beta =\frac{c}{a}$

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

$(x+1{)}^3+1^3$

$(x+1)(x^2+x+1)$

$⟹x=\frac{-1\pm \sqrt{1-4}}{2}=\frac{-1\pm 3i}{2}$

This happens when $a=b=c$