1. ## Express 2x^2-28x+53

Express 2x^2-20x+53 in the form 2(x-p)^2+q , where p and q are integers. not sure how to do this..

i factorised it and got this
2(x^2-10x)+53 plz help thx

2. Originally Posted by mike789
Express 2x^2-20x+53 in the form 2(x-p)^2+q , where p and q are integers. not sure how to do this..

i factorised it and got this
2(x^2-10x)+53 plz help thx
If:

$\displaystyle 2(x-p)^2+q=2x^2-4px+2p^2+q=2x^2-20x+53$

then $\displaystyle 4p=20$, so $\displaystyle p=5$, and $\displaystyle 2p^2+q=53$ so $\displaystyle q= .... ?$

CB

3. Originally Posted by mike789
i factorised it and got this
2(x^2-10x)+53 plz help thx
Good start! Now consider (x-5)² = x²-10x+25 which gives x²-10x = (x-5)²-25.

4. This question is essentially asking you to express that quadratic in "turning point form". This is done by completing the square.

Alternatively, you can "compare coefficients" described in CaptainBlack's post

5. $\displaystyle 2x^2 - 20x + 53$
$\displaystyle \equiv 2(x^2 - 10x) + 53$ // Take the 2 outside of the brackets
$\displaystyle \equiv 2((x-5)^2 - 25) + 53$ // Complete the square within the brackets
$\displaystyle \equiv 2(x-5)^2 - 50 + 53$ // Take the -25 outside the brackets
$\displaystyle \equiv 2(x-5)^2 + 3$ // Gather terms

6. Originally Posted by jgv115
This question is essentially asking you to express that quadratic in "turning point form". This is done by completing the square.

Alternatively, you can "compare coefficients" described in CaptainBlack's post
What I posted is completing the square, but done from first principles rather than remembering the algorithm, which I don't as it is a waste of brain space (same goes for a number of other things taught in common algebra and starting calculus, they are quicker to re-derive than to remember).

CB

7. Originally Posted by CaptainBlack
What I posted is completing the square, but done from first principles rather than remembering the algorithm, which I don't as it is a waste of brain space (same goes for a number of other things taught in common algebra and starting calculus, they are quicker to re-derive than to remember).

CB
Yes, yes. To CB you listen!

8. Originally Posted by CaptainBlack
What I posted is completing the square, but done from first principles rather than remembering the algorithm, which I don't as it is a waste of brain space (same goes for a number of other things taught in common algebra and starting calculus, they are quicker to re-derive than to remember).
If you are referring to remembering the formula for the coordinates of the turning point, I agree. But what I was hinting at post #3 doesn't really require remembering stuff at all.