math help... algerbra II?

Question

please, i need help with my homework. i have questions like these under, but i can not understand them. plzz help!!1

how do i evaluate the discriminant of these 2 problems?
and how do i tell how many salutions has, or whether the salutions are real or imaginary???

(2) = squere

y = 9x(2) - 24x

y = 4x(2) -3x +1

Answer 1

For the quadratic polynomial f(x) = ax^2 + bx + c
the discriminant, D = b^2 − 4ac

D < 0 implies the quadratic polynomial has no real roots
D = 0 implies the quadratic polynomial has two coincided real roots
D > 0 implies the quadratic polynomial has two distinct real roots

First question
y = 9x^2 - 24x
D = b^2 - 4ac
D = (-24)^2 - 4(9)(0)
D = 576
=> D > 0
therefore there are two distinct real roots(solutions)

Second question
y = 4x^2 - 3x + 1
D = b^2 - 4ac
D = (-3)^2 - 4(4)(1)
D = -7
=> D < 0
therefore there are no real roots(solutions)

Hope it helps :)

Answer 2

y=3x(3x^2-8)
x=0
x=sqrt(8/3)

this is real

y=4x^2-3x+1
use the quadratic equation and you will find that there is an imaginary root
This you can find by looking for the minima to show that the function never crosses the x axis.

For x=3/8 y=5/16 is the minima.
For every real value of x not equal to 3/8 (greater or less than) y is greater than 5/16

j

Answer 3

Equilibrium fee only skill to locate the place the two graphs intersect. Graph D and then Graph S and you have got it. (additionally you ought to easily set the two equations = to one yet another) -5p+40=-p^2 +30p-8 => 0=p^2-35p+40 8 Use quadratic equation to unravel: a=a million, b=-35, c=40 8 (-(-35)+ sqrt(-35^2-4(1x48))/(2*a million) = 33.fifty seven (-(-35)- sqrt(-35^2-4(1x48))/(2*a million) = a million.40 3 Plug in to ascertain... 33.fifty seven is unfavorable fee... not valid... a million.40 3 works... answer is a million.40 3

Answer 4

the first one i don't get... it has something wrong,
the rest, if it has a square, then it usually has 2 answers, real
if the square is neg. no solutions, and square roots that are neg, produce imaginary..... wait to see who else answers cause i am a little rusty.

Answer 5

That first answer is SO not right. (2) is saying it is squared. Read: 9 X squared.

Answer 6

y=9x(2)-24x
y=18x-24x
y=-6x
y/6=x
this one is not imaginary


y=4x(2)-3x+1
y=8x-3x+1
y=5x+1
y-1=5x
(y-1)/-5=x
this one is imaginary becasue you cannot divide by a negative number..........................hope this helps, and i hope i am right, it has been 5 or 6 yerars sdince i did this kind of work