Question

use the discriminant to determine the nature of the roots of 8x^2=0
a: no real roots c: one real root
b: two distinct real roots d: three distinct real roots

Answer 1

D = b^2 - 4ac

with D = discriminant

Answer 2

I don't know how to plug it in though, im horrible at math

Answer 3

8x^2=0
here, a = 8, b = 0, and c = 0
so,
D = b^2 - 4ac = 0^2 - 4(8)(0) = 0 - 0 = 0

because the discriminant (D) = 0, then it is one real root

Answer 4

oh ok! ok so I have another one -2x^2-5x-2=0
D= b^2-4ac= 0^2 -4(-2)(0)= 0-0=0????

Answer 5

Or do I put for b -5 and for c I put -2?

Answer 6

the general form of quadratic equation is
ax^2 + bx + c = 0
so, if given -2x^2-5x-2=0 it means
a = -2, b = -5, and c = -2

Answer 7

yeah, a = -2, b = -5, and c = -2
now plug in into formula of D
D = b^2 - 4ac

Answer 8

So D=-5^2 -4(-2)(-2)

Answer 9

yeah,
D=(-5)^2 -4(-2)(-2)
D = 25 - 16
D = 9
it means D > 0, right ?

Answer 10

I can get the solving part after awhile but what I have trouble with is how do I tell how many roots an equation has

Answer 11

there are 3 kinds of roots of quadratic equation :
1) if D > 0 then it has 2 distinct real roots
2) if D = 0 then it has one real root (for example see in your question before)
3) if D < 0 then it has no real roots (or you can call it has 2 imaginary roots)

Answer 12

Ok dumb question but how do I know if its <, =, >?

Answer 13

and dont think this would has three distinct real roots, because the quadratic equation only has maximum 2 roots

see, if
D = 0 obvious it is the first kind, lol
D = 9, 16, 25, 48, 127, 999, or all positive numbers (it is D >0)
D = -2, -33, -25, or all negative numbers ( it is D <0)

Answer 14

in other words, < 0 actually negative number and
> 0 it is positive number

Answer 15

Got it!!! Thank you very much!!! Wow!! Thanks again!

Answer 16

does that helps ?

Answer 17

you're welcome :)