How many real number solutions does this equation have?

Question

0= 5x^2 +2x - 12

A. one solution

B. two solutions

C. infinite many solutions

D. no solutions

Answer 1

The equation is in the form of a quadratic equation, which can be solved using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For the given equation, a = 5, b = 2, and c = -12.

Plugging these values into the quadratic formula, we get:

x = (-2 ± √(2^2 - 4*5*-12)) / (2*5)
x = (-2 ± √(4 + 240)) / 10
x = (-2 ± √(244)) / 10
x = (-2 ± 2√61) / 10

Since the discriminant (b^2 - 4ac) is positive, there are two distinct real number solutions.

Therefore, the answer is B. two solutions