How many real number solutions does the equation have?
0=5x^2+2x-12
3 answers
This equation has two real number solutions.
Why?
We can solve for x by factoring or using the quadratic formula:
Factoring:
0=5x^2+2x-12
0=(5x-6)(x+2)
So the solutions are x = 6/5 and x = -2.
Using the quadratic formula:
0=5x^2+2x-12
x = (-b ± sqrt(b^2 - 4ac)) / 2a
x = (-2 ± sqrt(2^2 - 4(5)(-12))) / 2(5)
x = (-2 ± sqrt(244)) / 10
x = (-2 ± 2*sqrt(61)) / 10
Simplifying, we get x = 6/5 and x = -2, which are the same solutions as before.
Therefore, the equation has two real number solutions.
Factoring:
0=5x^2+2x-12
0=(5x-6)(x+2)
So the solutions are x = 6/5 and x = -2.
Using the quadratic formula:
0=5x^2+2x-12
x = (-b ± sqrt(b^2 - 4ac)) / 2a
x = (-2 ± sqrt(2^2 - 4(5)(-12))) / 2(5)
x = (-2 ± sqrt(244)) / 10
x = (-2 ± 2*sqrt(61)) / 10
Simplifying, we get x = 6/5 and x = -2, which are the same solutions as before.
Therefore, the equation has two real number solutions.