Question

If we can factorise ax² + bx + c , a is not equal to zero, into a product of two linear factors, then the roots of the quadratic equation ax² + bx +c =0 can be found by equating each factor to zero.. explain .

Answer 1

for example x - 1 is the factor of any equation... then by equating it with zero (x - 1 = 0)...
which becomes x = 1
so 1 is the root of that equation...

Answer 2

The given quadratic equation is ax2+bx+c

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

ax2+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.