Question

How many solutions does f(x) = 5x2+2x–12

Answer 1

Answer: 2 different real number solutions

Both solutions are irrational.

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Explanation:

The given function f(x) = 5x^2+2x-12 is in the form f(x) = ax^2+bx+c

We see that

a = 5, b = 2, c = -12

Plug those values into the discriminant formula below

D = b^2 - 4ac

D = (2)^2 - 4(5)(-12)

D = 4 - 4(5)(-12)

D = 4 + 240

D = 244

Because D > 0, this means we have two different real solutions for f(x) = 0

The value of D is not a perfect square, so those two solutions or roots are irrational.