Find the Discriminant f(x)=25x^2-10x+1

$f (x) = 25 x^{2} - 10 x + 1$

Step 1

The discriminant of a quadratic is the expression inside the radical of the quadratic formula.

$b^{2} - 4 (a c)$

Step 2

Substitute in the values of $a$ , $b$ , and $c$ .

${(- 10)}^{2} - 4 (25 \cdot 1)$

Step 3

Evaluate the result to find the discriminant.

Simplify each term.

Raise $- 10$ to the power of $2$ .

$100 - 4 (25 \cdot 1)$

Multiply $- 4 (25 \cdot 1)$ .

Multiply $25$ by $1$ .

$100 - 4 \cdot 25$

Multiply $- 4$ by $25$ .

$100 - 100$

Subtract $100$ from $100$ .

$0$