Algebraic methods

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tindall19
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#1
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#1
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?
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zetamcfc
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#2
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#2
(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.
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ashvinsingh
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#3
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#3
(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?
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tindall19
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#4
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#4
(Original post by ashvinsingh)
Hint - repeated roots means the discriminate = 0 , can you remember how to work out the discriminate?
not a clue!
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tashe7
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#5
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#5
(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
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mqb2766
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#6
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#6
(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/q...-equation.html
Last edited by mqb2766; 1 month ago
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