Question

True or false? The quadratic equation 10p2 - 5p = -8 has one solution.

Answer 1

Answer: False

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Explanation:

I'll use x in place of p.

The original equation 10x^2-5x = -8 becomes 10x^2-5x+8 = 0 after moving everything to one side.

Compare this to ax^2+bx+c = 0

We have

• a = 10
• b = -5
• c = 8

Plug those three values into the discriminant formula below

d = b^2 - 4ac

d = (-5)^2 - 4(10)(8)

d = 25 - 40*8

d = 25 - 320

d = -295

The discriminant is negative, which means we have no real solutions. If your teacher has covered complex or imaginary numbers, then you would say that the quadratic has 2 complex roots. If your teacher hasn't covered this topic yet, then you'd simply say "no real solutions".

Either way, this quadratic doesn't have exactly one solution. That only occurs when d = 0. Therefore, the original statement is false.