If $\alpha$ is a root of the quadratic equation $ax^2+bx+c=0$ with $a\…

Question

If $\alpha$ is a root of the quadratic equation $ax^2+bx+c=0$ with $a
eq 0$, then which statement must be true?

Accepted Answer

B. $a\alpha^2+b\alpha+c=0$

By definition, a real number $\alpha$ is a root of $ax^2+bx+c=0$ if substituting $x=\alpha$ makes the equation true. Therefore, $a\alpha^2+b\alpha+c=0$.

Answer

$a\alpha+b\alpha+c=0$

Answer

$\alpha^2+\alpha+1=0$

Answer

$a+b+c=0$

If $\alpha$ is a root of the quadratic equation $ax^2+bx+c=0$ with $a\neq 0$, then which statement must be true?