Browsing category quadratics

Cowboy Completing The Square

Factorising a quadratic? It's nice when it comes off, but there's a lot of guesswork, and no guarantee it even factorises. Completing the square? Who has time for all that algebra? And as for the quadratic formula, or your clever calculator methods: honestly, what are you, an engineer? There is

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Ask Uncle Colin: Complex quadratics with real values

Dear Uncle Colin, I was wondering: given a quadratic function with real coefficients, what complex arguments lead to real answers? - Researching Equations And Lines Hi, REAL, and thanks for your message! This turns out to be simpler than I expected: if you have a quadratic $f(z) = az^2 +

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An “Impossible” New Zealand exam: Part II

Last time, we looked at an 'impossible' question from a New Zealand exam, which was (of course) nothing of the sort. The second question highlighted as a brute was this one: (Full exam is here.) But, you see, I look at that and think... part (iv) isn't straightforward on its

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An unexpected connection

You want to know one of my favourite things about maths? It's the connections. Connections between things that don't, on the face of it, seem remotely connected. One just cropped up, and made me grin from ear to ear, so I thought I'd share it with you. The Parker Square

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Ask Uncle Colin: Shouldn’t this be simple?

Dear Uncle Colin, I've got a funny square and I can't find $x$. Can you help? - Oughta Be Simple, Can't Unravel Resulting Equations Hi, OBSCURE, and thanks for your message! You're right, it ought to be simple... but it turns out not to be. It is simple enough to

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Ask Uncle Colin: An Absurd Quadratic

Dear Uncle Colin, In a recent exam, I was invited to solve $12x^2 - 59x + 72=0$ without a calculator. Is that a reasonable thing to ask? Very Irate EdExcel-Taught Examinee Hi, VIETE, and I don't blame you for being cross - in a non-calculator exam, I'm not sure that

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Ask Uncle Colin: A Complex Conundrum

Dear Uncle Colin, I'm told that $z=i$ is a solution to the complex quadratic $z^2 + wz + (1+i)=0$, and need to find $w$. I've tried the quadratic formula and completing the square, but neither of those seem to work! How do I solve it? - Don't Even Start Contemplating

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Ask Uncle Colin: A Quadratic Conjecture

Dear Uncle Colin, My teacher suggested that if you factorise a quadratic and add the brackets, you get the derivative. I am now too frightened to sleep. -- Quadratic Understanding Is Not Easy Hi, QUINE, and thanks for your message! To take a simple example, $x^2 + 5x + 6

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On quadratic sequences

This is a guest post from Mark Ritchings, a maths tutor in Bury. A quadratic sequence is a sequence for which the $n$th term is $an^2+bn+c$. The constants $b$ and/or $c$ might be zero but $a$ definitely isn't. The first term is $a\times 1^2 +b \times 1 + c =

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An interesting GCSE triangle

It's not often I have anything nice to say about EdExcel. I've usually found their exams to be the most predictable and least thought-provoking of all the boards (at least until they finally snapped in 2013 and let Kate the Photographer loose on an unsuspecting cohort). At GCSE, their advanced

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