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

they are two different problems! is there anybody here that can actually help me??
i need to stupid answers please!

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 genuine y=4x^2-3x+a million use the quadratic equation and you will locate that there is an imaginary root This you will come across by making use of searching for the minima to tutor that the function in no way crosses the x axis. For x=3/8 y=5/sixteen is the minima. for each genuine fee of x not equivalent to 3/8 (extra desirable or decrease than) y is extra desirable than 5/sixteen j

Answer 3

First of all, you need to realize that the solutions to these equations are curves, not numbers. These equations descibe parabolas if you were to graph them. There is a technique called "finding the zeros" which means finding the place on the curve where y=0. In this way you will generate specific points on the x axis. So set these equations equal to zero and then apply the binomial theorem: (-b+-sqrt(b2-4ac))/2a and see if the solutions are real or imaginary. They will only be imaginary if b2-4ac is a negative number. I hope this helps.

Answer 4

settle them both equal

9x(2) - 24x = 4x(2) - 3x + 1
5x(2) - 21x - 1= 0

then you could use your T-1 or evaluate with some othe method