Question

Find the sum and product of the roots of the quadratic equation: $x^2-5x+8=0$.

Answer 1

Step 1: Compare the given equation with the general form of a quadratic equation:

Given equation: $x^2-5x+8=0$.

The general form of a quadratic equation is $a{x}^2+bx+c=0$.

Thus, $a=1,b=-5,c=8$.

Step 2: Find the sum of the roots:

It is known that the sum and product of the roots of the quadratic equation $a{x}^2+bx+c=0$ are given by $\left(-\frac{b}{a}\right)$ and $\left(\frac{c}{a}\right)$ respectively.

Thus, the sum of the roots of given quadratic equation is $\left(-\frac{b}{a}\right)=\left(-\frac{-5}{1}\right)=5$.

And the product of the roots of given quadratic equation is $\left(\frac{c}{a}\right)=\left(\frac{8}{1}\right)=8$.

Therefore, the sum of the quadratic equation is $5$ and the product of the quadratic equation is $8$.