Question

State whether True or False

If we can factorize $a{x}^2+bx+c,a\ne 0$, into a product of two linear factors, then the roots of the quadratic equation $a{x}^2+bx+c=0$ can be found by equating each factor to zero ?

• A. True
• B. False

Answer 1

The correct option is A True

The given quadratic equation is $a{x}^2+bx+c$

Let us write this quadratic equation into a product of two linear factors i.e.

$a{x}^2+bx+c=(x+d)(x+e)$

Then the roots of this quadratic equation are $-d$ and $-e$ which we get using $x+d=0$ and $x+e=0$.

So, we get the roots by equating each factors to zero.

Hence, the given statement is true.