Use the quadratic formula to find all real solutions of the equation.
A) x = 10, x = 4
B) x = 5, x = -2
C) x = 5, x = 4
D) x = -5, x = 2
E) x = 5, x = 2

Question

Use the quadratic formula to find all real solutions of the equation. 
A) x = 10, x = 4 
B) x = 5, x = -2 
C) x = 5, x = 4 
D) x = -5, x = 2 
E) x = 5, x = 2

Quizplus · Accepted Answer

Since the quadratic formula is used to find solutions for quadratic equations in the form ax^2+bx+c=0, we need to first put the given equation into this form:

x^2 - 7x - 10 = 0

Using the quadratic formula: 
x = (-b ± sqrt(b^2 - 4ac)) / 2a

We plug in a = 1, b = -7, and c = -10, then simplify:

x = (7 ± sqrt(49 + 40)) / 2
x = (7 ± sqrt(89)) / 2

These solutions are both real numbers, and they match the options E) x = 5, x = 2.

Use the Quadratic Formula to Find All Real Solutions of the Equation