Question

How many solutions does this equation have

Answer 1

Answer:

Two solutions

Step-by-step explanation:

This is a quadratic equation in the form y = ax² + bx + c.

For quadratic equations, you can find solutions using the quadratic formula:

$x = \frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

To find the number of solutions, you only need what's inside the square root. We call it the "discriminant" because lets us know the number of solutions without solving.

$b^{2}-4ac$

If b²- 4ac > 0, two solutions. (greater than)

If b²- 4ac < 0, no solutions. (less than)

If b²- 4ac = 0, one solution. (equal to)

y = ax² + bx + c

y = -3x² + x + 12

a = -3   b = 1   c = 12

Substitute into the discriminant

b²- 4ac

= 1² - 4(-3)(12)

= 1 - (-144)

= 145 > 0

b²- 4ac > 0                Discriminant greater than 0

Therefore, there are two solutions.