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Roots Question

I have this question on my maths assignment, I’m pretty sure you have to use 0 < b^2 + 4ac to to find the values of k, but I cannot figure out what a, b, and c are! Any help would be greatly appreciated.

𝑦 = (𝑥 − 𝑘)^2 + 10𝑘 has real roots when 𝑦 = 0, find the set of possible values of k.
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Pangol
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Original post by georgiapage1
I have this question on my maths assignment, I’m pretty sure you have to use 0 < b^2 + 4ac to to find the values of k, but I cannot figure out what a, b, and c are! Any help would be greatly appreciated.

𝑦 = (𝑥 − 𝑘)^2 + 10𝑘 has real roots when 𝑦 = 0, find the set of possible values of k.


You are (very nearly) right about what you have to do. Notice that the question says that the equation has real roots - this doesn't necessarily mean that it has two distinct real roots.

To find a, b and c, expand the bracket and write what you get in the form ax^2 + bx + c. It might look slightly trickier than you are expecting, but focus on how many x^2's you have, how many x's you have, and what the constant term on the end is.
Original post by Pangol
You are (very nearly) right about what you have to do. Notice that the question says that the equation has real roots - this doesn't necessarily mean that it has two distinct real roots.

To find a, b and c, expand the bracket and write what you get in the form ax^2 + bx + c. It might look slightly trickier than you are expecting, but focus on how many x^2's you have, how many x's you have, and what the constant term on the end is.

Thank you :smile:

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