Question

If the equations $a{x}^2+bx+c=0and{x}^2+x+1=0$ have a common root, then

• A. a + b + c = 0
• B. a = b or b = c or c = a
• C. a – b + c = 0
• D. a = b = c

Answer 1

The correct option is D a = b = c

$x^2+x+1=0$ has roots $\omega ,{\omega }^2$.
$\therefore a{x}^2+bx+c=0$
$\therefore$ Both roots common
$=\frac{a}{1}=\frac{b}{1}=\frac{c}{1}$