use the zero product property to find the solutions to the equation $x^{2}-13x + 30 = 0$.\n$x=-10$ or…

use the zero product property to find the solutions to the equation $x^{2}-13x + 30 = 0$.\n$x=-10$ or $x=-3$\n$x=-10$ or $x = 3$\n$x=-3$ or $x = 10$\n$x = 3$ or $x = 10$

use the zero product property to find the solutions to the equation $x^{2}-13x + 30 = 0$.\n$x=-10$ or $x=-3$\n$x=-10$ or $x = 3$\n$x=-3$ or $x = 10$\n$x = 3$ or $x = 10$

Answer

Explanation:

Step1: Factor the quadratic equation

We need to find two numbers that multiply to 30 and add up to 13. The numbers are 3 and 10. So, $x^{2}-13x + 30=(x - 3)(x - 10)=0$.

Step2: Apply the zero - product property

If $ab = 0$, then either $a = 0$ or $b = 0$. So, if $(x - 3)(x - 10)=0$, then $x-3=0$ or $x - 10=0$.

Step3: Solve for x

For $x-3=0$, we get $x=3$. For $x - 10=0$, we get $x=10$.

Answer:

$x = 3$ or $x = 10$