# How to find the root of a quadratic formula

## Homework Statement

(A) For what value of K does the equation 2x^2-10x +8 = K have a repeated root? Use the quadratic formula to find the root.

(B) Choose a value for K so the equation has no real roots, Use the quadratic formula to prove that this equation has no real roots for your chosen value for K.

this is a question i was given and to be honest i am stumped, i understand what a root is, but im unsure of how to find a repeated root. any help is appreciated!

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Do you know the quadratic formula? What would have to be the value of b2-4ac to have a repeated root?

the formula above is the quadratic formula for both (A) and (B)

y=2x^2-10x+8

No, the quadratic formula is a way to solve (i.e., find the solutions of) ax2+bx+c = 0

this is the whole question i was given.

2 a) draw the graph of the quadratic y=2x^2-10x+8

2 b) solve the equation 2x^2-10x+8=K when K=0

2 c) For what value of K does the equation 2x^2-10x +8 = K have a repeated root? Use the quadratic formula to find the root.

2 d) Choose a value for K so the equation 2x^2-10x +8 = K has no real roots, Use the quadratic formula to prove that this equation has no real roots for your chosen value for K.

does that help at all?

SteamKing
Staff Emeritus
Homework Helper
druuuuuuuunnk, you will have to change to soooooooober so that you can think about solving this problem.

PeterO
Homework Helper
this is the whole question i was given.

2 a) draw the graph of the quadratic y=2x^2-10x+8

2 b) solve the equation 2x^2-10x+8=K when K=0

2 c) For what value of K does the equation 2x^2-10x +8 = K have a repeated root? Use the quadratic formula to find the root.

2 d) Choose a value for K so the equation 2x^2-10x +8 = K has no real roots, Use the quadratic formula to prove that this equation has no real roots for your chosen value for K.

does that help at all?
SO have you done part (a) - it would be useful to factorise the quadratic in order to do that.

Ok, I see where the confusion is. You might want to look at the part of the link that is called http://en.wikipedia.org/wiki/Quadratic_equation" [Broken].

Then, the question is asking, for what value of K does the quadratic formula give repeated roots?

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HallsofIvy
Homework Helper

NascentOxygen
Staff Emeritus
A quadratic can have two roots, or no roots. (Or to put it more exactly: two real roots, or no real roots.)

If the real roots are equal, then this can be referred to has having a repeated root. So all you need to do is determine that value of K which causes there to be zero difference between the two roots.

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ok so I've been doing some reading, i now know that i use the quadratic forumla to solve the quadratic equation in part B. i got x=4 and x=1

for part C, do i change the quadratic equation 2x^2-10x+8=K. by this i mean do i need to make it 3x^2-11x+9=K or somthing like that, until i find a equation that has two roots which are the same?

im not gonna lie to you guys, once i've done this maths course work i pass my year and i never have to do maths at this level again. Im doing product design at university. its basically just drawing lol.

Im terrible at maths, my uni are making me do a foundation year or maths and physics, they are not my strong points, if you could just tell me the answer i would appriate it, this course works in for tomorrow and its worth 50% of my final grade. if i get 80% of this course work right i pass the year.

eumyang
Homework Helper
for part C, do i change the quadratic equation 2x^2-10x+8=K. by this i mean do i need to make it 3x^2-11x+9=K or somthing like that, until i find a equation that has two roots which are the same?
No. You move the K to the other side, and let c = 8 - K in the quadratic formula. You'll notice that in order for you to have a repeated root, the expression underneath the square root, b2 - 4ac, must equal 0. Look up discriminant.

Im terrible at maths, my uni are making me do a foundation year or maths and physics, they are not my strong points, if you could just tell me the answer i would appriate it, this course works in for tomorrow and its worth 50% of my final grade. if i get 80% of this course work right i pass the year.
No, we're not allowed to just give the answers. You need to show the work to us first, and then we help you. That's the forum rules.

Mark44
Mentor
Im terrible at maths, my uni are making me do a foundation year or maths and physics, they are not my strong points, if you could just tell me the answer i would appriate it, this course works in for tomorrow and its worth 50% of my final grade. if i get 80% of this course work right i pass the year.

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it was worth a try :P

HallsofIvy