Use the discriminant to determine how many and what kind of solutions the quadratic equation 2x2 - x = - 4 has.

Hey there! I'm happy to help!

Our quadratic equation is 2x²-x=-4. Quadratics follow the form ax²+bx+c=0, so our a is 2, our b is -1, and our c is 4 (add 4 to both sides so we have 2x²-x+4=0, fitting the format).

The discriminant of a quadratic equation is b²-4ac. Here's how to figure out how many and what kind of solutions the equation has given the quadratic equation. I'll call the discriminant D.

If D>0, there are 2 real roots.

If D=0, there is 1 real root.

If D<0, there are 2 complex roots.

So, let's look at our discriminant.

-1²-4(2×4)

1-4(8)

1-32

-31

Our discriminant is less than 0, so we have 2 complex solutions.

Have a wonderful day! :D

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