Question

Use the discriminant to determine the number of real solutions to the quadratic equation. −u2+2u−5=0 What is the number of real solutions? Select the correct answer below: 0 1 2

Answer 1

Sqrt (4-4*-1*-5), = plus or minus 4i

Answer 2

Answer: None, 0 real roots

Explanation:

To find the discriminant, you simply do
`b^2 - 4ac`

b = 2

a = -1

c = -5

`2^2-4(-1)(-5) = 4 - 20 = -16`

iff x > 0: 2 roots

iff x < 0: none

iff x = 0: 1 root

Actual Explanation and Intuition behind it:

If the answer is negative, you cant take the square root of the number. Because no matter what, you will always strive for a positive number. Unless you implement calculus, but that is way beyond a middle schoolers level

If the answer is postive, there will be 2 roots because you can make x itself equal to a negative number because when you square it, it will be positive. So the positive and negative value will be an acceptable answer

If the answer is 0, then youre basically doing the square root of 0. Thats equal to 0

The discriminant formula itself comes straight from the quadratic formula, which you should memorize because it is extremely useful.
`(-b (+/-) √(b^2-4ac) )/(2a)`