Chapter A.6, Problem 126AYU

To determine

To find: Whether each quadratic equation has two unequal real solutions, a repeated real solution, or no real solution without solving the equation: $25x^2-20x+4=0$.

Answer to Problem 126AYU

Repeated real solution.

Explanation of Solution

$25x^2-20x+4=0$

$a{x}^2+ bx + c = 0$ Compare to standard form.

With $a=25, b=-20$, and $c=4$, the discriminant is $b^2-4ac={\left(20\right)}^2-4\left(25\right)\left(4\right)=0$.

Since $b^2-4ac=0$, there is repeated real solutions.