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You're probably familiar with the formula for solving a quadratic equation, ax² + bx + c = 0. If not, here it is; you'll certainly need to know it by the time you do your exam.
But you may have wondered if there are also formulae for cubic equations (with x³), quartic (x⁴) and so on.
The answer is yes and no. While the quadratic formula is short enough to memorize, the cubic one is long and horrible - so long and horrible, in fact, that I'll simply point you this page, rather than trying to reproduce it here. But you can relax, it's not in the A-level course.
And there is even a formula, or at least a procedure, for the quartic, but that's still worse. It involves converting the original equation into what's called depressed quartic form, which is undoubtedly how you too will feel when you see all the algebra involved. I advise staying well away from it.
For quintics (x⁵) and above, the formula is so complicated that even God can't work it out - which is another way of saying that it doesn't exist. The Norwegian mathematician Niels Abel, who tragically died of tuberculosis at the young age of 26, proved that was the case in 1824, in what is called Abel's Impossibility Theorem. That's quite something to be remembered for; if you can't solve a problem, surely the next best thing is to prove it can't be solved by anyone else either.
The good news is that you will not have to master anything as complex as this to do well in your maths A-level. But some tutoring might help. To discuss that, why not get in touch?
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