Chapter A.6, Problem 123AYU

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: $x^2-5x+7=0$.

Answer to Problem 123AYU

No real solution.

Explanation of Solution

$x^2-5x+7=0$

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

With $a=1, b=-5$, and $c=7$, the discriminant is $b^2-4ac={(-5)}^2-4\left(1\right)\left(7\right)=-3$.

Since $b^2-4ac<0$, there is no real solution.