Question

Help with discriminants?
Harry is competing in the triwizard tournament at hogwarts. One of the challenges he faces is to analyze the discriminant of the quadratic equation h(x) = x^2 - 2x - 35. Unfortunately, harry skipped algebra class last week to try out his new quidditch broom with his friends, so he is a little rusty on his math skills. Which of his friends should Harry take the advice of? (hint: two friends are correct) (friends advice in image posted below)

Answer 1

hmmm.... and this is in a math book?

Answer 2

No, this is something my teacher made up.

Answer 3

do you know how to calculate the discriminant?

Answer 4

No, I don't.

Answer 5

ok the general for of the quadratic equation is

ax^2 + bx + c = 0

a,b and c are constants

the discriminant is b^2 - 4ac

its value will tell you the nature of the roots of the equation

Answer 6

so if you plug in a = 1, b=-2 and c = -35 you can work it out

Answer 7

Ok, let me try

Answer 8

-2^2 - 4(1)(-35)
-4 - 140
-144
Is that right?

Answer 9

@cwrw238

Answer 10

no you have the right values plugged in but b^2 = (-2)^2 = 4
and -4ac = - 4*1*-35 = 140

a minus times a minus = a plus

Answer 11

so correct is 4 + 140 = 144

Answer 12

Ah I thought so

Answer 13

So where do I go from here with this question?

Answer 14

well as the discriminant is positive the roots are real so can you tell me which of the 2 friends are wrong?

Answer 15

Well just by looking at it Ron is one of the wrong friends

Answer 16

@cwrw238

Answer 17

right - he said D = -136

Answer 18

so then hermione would be correct? because 144 is a perfect square

Answer 19

and the roots are real - not complex

Answer 20

right about Hermione

Answer 21

sorry Guy i gotta go right now
you are on the right track...

Answer 22

Oh so if the roots are real, Neville is wrong

Answer 23

Right?

Answer 24

yes Hagrid is right

Answer 25

Neville is wrong

Answer 26

Thanks so much for all of your help