Find the Sum and Product of the Roots of the Quadratic Equation x^2=10x-25

$x^{2} = 10 x - 25$

Step 1

Find $a$ , $b$ , and $c$ .

Move all the expressions to the left side of the equation.

Subtract $10 x$ from both sides of the equation.

$x^{2} - 10 x = - 25$

Add $25$ to both sides of the equation.

$x^{2} - 10 x + 25 = 0$

Once the quadratic is in standard form, the values of $a$ , $b$ , and $c$ can be found.

$a x^{2} + b x + c$

Use the standard form of the equation to find $a$ , $b$ , and $c$ for this quadratic.

$a = 1$ , $b = - 10$ , $c = 25$

Step 2

Substitute the values into the sum of roots formula $- \frac{b}{a}$ .

Divide $10$ by $1$ .

$10$

Step 3

Substitute the values into the product of roots formula $\frac{c}{a}$ .

Divide $25$ by $1$ .

$25$

Step 4

List the results.

Sum of the roots is $10$

Product of the roots is $25$