Question

describe the discriminant and the nature of the roots: y=-2x^2-4x+5

Answer 1

please also explain

Answer 2

your equation is in the form : \(ax^2+bx+c=0\)

Therefore you can find your roots by using the discriminant, \(b^2-4ac\), testing whether it's greater than, less than or equal to 0.

Answer 3

First you want to identify \(a~,~ b ~,~ c\).

Answer 4

so -24?

Answer 5

hello?

Answer 6

Are you sure it's -24?

Answer 7

Can you identify what a, b, and c are for me?

Answer 8

with -2x being a, -4x being b, and 5 being c yes

Answer 9

Alright, then \(b^2-4ac = (-4)^2 -4((-2)(5)) = 16 +40 = 56\)

Answer 10

I think what you had done was 16 - 40.

Answer 11

Are you following?

Answer 12

@mathacomplice ?

Answer 13

oh sorry yes

Answer 14

i was getting something to eat

Answer 15

So the discriminant tells us if:

\(b^2-4ac > 0\)

We will have \(\color{red}{\text{2 real solutions}}\) ONLY IF we factor our quadratic and end up with a perfect square.

\(b^2-4ac = 0\)

and your function is NOT a perfect square, then you will have \(\color{red}{\text{2 real irrational solutions}}\)

\(b^2 -4ac < 0\)

Your function will have no \(\color{red}{\text{real}}\) solutions, but \(\color{red}{\text{2 imaginary/complex solutions}}\)

Answer 16

Our discriminant: \(b^2 -4ac = 56 \implies 56 >0\) Therefore we have 2 real solutions.

Answer 17

Understand @mathacomplice ?

Answer 18

ahh, yes thank you very much

Answer 19

No problem :)