Question

Compute the value of the discriminant and give the number of real solutions of the quadratic equation.

Answer 1

discriminant
b-4ac

Answer 2

the discriminant is,
\(\normalsize\color{ slate }{\Huge{\bbox[5pt, lightcyan ,border:2px solid black ]{ \LARGE{x=~} \huge{ \color{magenta}{b} ^2-4 \color{blue}{a} \color{red}{c}}~ }}}\)

when the equation is \(\LARGE\color{black}{ \color{blue}{a} x^2+ \color{magenta}{b}x+ \color{red}{c}=0 }\).

Answer 3

\[-4x^2+8x-1\]

Answer 4

this is the equation

Answer 5

a=-4
b=8
c=-1

plug this in =b-4ac

Answer 6

so

Answer 7

\[-8\pm \sqrt{64-16}\]

Answer 8

I am not sure

Answer 9

\(\bbox[8pt, lime,border:8px solid black]{\LARGE \LARGE{x=~} \huge{ \frac{-\color{magenta}{b} \pm\sqrt{ \color{magenta}{b} ^2-4 \color{blue}{a} \color{red}{c}}}{2 \color{blue}{a}} } ~ }\)

when the equation is \(\LARGE\color{black}{ \color{blue}{a} x^2+ \color{magenta}{b}x+ \color{red}{c}=0 }\).

(I think you are missing some part of the quadratic formula)

Answer 10

oh
all over -8

Answer 11

yes

Answer 12

Yeah. Now can you solve it further?

Answer 13

yeah

Answer 14

Alright. :)

Answer 15

\[\frac{ -2\pm \sqrt{3} }{ 2 }\]

Answer 16

@uri
@SolomonZelman

Answer 17

@uri
@SolomonZelman

Answer 18

@uri
@SolomonZelman

Answer 19

Must be right!

Answer 20

so then what is the value of the descriminant and the number of real solutions

Answer 21

@Nnesha
@SolomonZelman
@TheSmartOne

Answer 22

The value of the discriminant is simply the value under the square root in the quadratic formula. Here I will call it \( \Delta \) (because that is what I am used to labelling it as; others might use d or D instead).

\( x = \dfrac{-b \pm \sqrt{\color{goldenrod}{b^2 - 4ac}}}{2a} = \dfrac{-b \pm \sqrt{\color{goldenrod}\Delta}}{2a} \)

\( \begin{align} \Delta &= b^2 - 4ac \\ &= (8)^2 - 4(-4)(-1) \\ &= 64 - 16 \\ &= 48 \end{align} \)

The discriminant tells you the number of real solutions based on its sign value. Think about how the quadratic formula is affected by the value there. If it is negative, the square root of a negative is not a real number!
\( \Delta > 0 \), the quadratic has two unique real solutions
\( \Delta = 0 \), the quadratic has one repeated solution (so, there are two but they are the same).
\( \Delta < 0 \), the quadratic has no real solutions (two complex solutions)

Answer 23

help me
is the discriment \[\frac{ \pm 1 \sqrt{3} }{ -2 }\]

Answer 24

Here, the discriminant's value is 48 (remember, \(b^2 - 4ac \) is the discriminant), so the sign is positive. Thus, the solutions would be as indicated above.

Answer 25

so the descriminant is 48 and there are 2 unique real solutions

Answer 26

Yup. b^2 - 4ac = (8)^2 - 4(-4)(-1) = 64 - 16 = 48. 48 > 0, so sqrt(48) is a real number and there are two real number solutions to the quadratic!

Answer 27

ok thanks yay

Answer 28

No problem! :)

Answer 29

Sorry,I was away but @AccessDenied helped. cx

Answer 30

thx anyways ;)