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Algebraic methods

Not sure if I'm being an idiot here but not really sure what this question wants me to do:
The quadratic equation x² + (3k + 1)x + (4 – 9k), where k is constant, has repeated
roots.
Show that 9k² + 42k – 15 = 0.

I originally thought it wanted me to find the values of k but that's the second part to the question. What does "show that" even mean in this case?
Original post by tindall19
Not sure if I'm being an idiot here but not really sure what this question wants me to do:
The quadratic equation x² + (3k + 1)x + (4 – 9k), where k is constant, has repeated
roots.
Show that 9k² + 42k – 15 = 0.

I originally thought it wanted me to find the values of k but that's the second part to the question. What does "show that" even mean in this case?

Discriminant.
Original post by tindall19
Not sure if I'm being an idiot here but not really sure what this question wants me to do:
The quadratic equation x² + (3k + 1)x + (4 – 9k), where k is constant, has repeated
roots.
Show that 9k² + 42k – 15 = 0.

I originally thought it wanted me to find the values of k but that's the second part to the question. What does "show that" even mean in this case?

Hint - repeated roots means the discriminate = 0 , can you remember how to work out the discriminate?
Reply 3
Avatar for tindall19
tindall19
OP
2
Original post by ashvinsingh
Hint - repeated roots means the discriminate = 0 , can you remember how to work out the discriminate?

not a clue!
Reply 4
Avatar for tashe7
tashe7
4
Original post by tindall19
not a clue!

b^2 - 4ac, where a is the coefficient of k^2, b is the coefficient of k and c is the -15
Reply 5
Avatar for mqb2766
mqb2766
21
Original post by tashe7
b^2 - 4ac, where a is the coefficient of k^2, b is the coefficient of k and c is the -15

a, b and c refer to the coefficients of the original quadratic in x, not the quadratic in k you're trying to show.

So, using the quadratic formula to solve the original quadratic equation in x, the two roots are equal if the discriminant = 0 so
b^2 - 4ac = 0
so sub in the a, b and c which are functions of k and rearrange to get the desired quadratic (in k) equation.

@tindall19 if you really don't have a clue, its worth going over that section of your notes again or as a starter
https://www.mathsisfun.com/algebra/quadratic-equation.html
(edited 2 years ago)

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