Question

Why do the roots of a quadratic equation have the opposite sign of the factors of a quadratic equation

Answer 1

To find the roots of the quadratic equation we set the factors of the quadratic equation equal to 0.

Explanation:

Consider the provided information.

Roots of the equation is x-intercepts or zeros of the given equation.

So, By definition, the value of The y-coordinate is zero for points situated on the x-axis.

Thus, we can find the roots of a quadratic function, by putting f (x) = 0.

Now, let (x-a)(x-b) is the factor of any quadratic equation.

To find the roots of the quadratic function we will put our factor equal to 0.

`(x-a)(x-b)=0`

Now by the zero product property either x-a=0 or x-b=0

`x-a=0` then
`x=a`

or

`x-b=0` then
`x=b`

So, we can say that to find the roots of the quadratic equation we set the factors of the quadratic equation equal to 0.