# Maths - Quadratics Tips and Tricks

> Source: https://ollybritton.com/notes/a-level/maths/topics/quadratic-tips-and-tricks/ · Updated: 2020-10-03 · Tags: maths

##### How can you solve something like $-x^2 + 7x - 15$??
Take out $-1$ as a factor.

##### What is the result of taking out $-1$ from $15 + 13x - 4x^2$??
$$
-(4x^2 - 13x - 15)
$$

##### How can you solve something like $x^4 + 5x^2 - 36 = 0$??
Substitute $a = x^2$.

##### Substitute $a = x^2$ into $x^4 + 5x^2 - 36 = 0$??
$$
a^2 + 5a - 35 = 0
$$

##### How could you solve something like $x - 9\sqrt{x} + 24 = 0$??
Substitute $a = x^{\frac{1}{2}}$.

##### Substitute $a = x^{\frac{1}{2}} into $x - 9\sqrt{x} + 24 = 0$??
$$
a^2 - 9a + 24
$$

##### What is the name for a quadratic in disguise??
A sneaky quad.

##### What are the two criteria for an equation being a sneaky quad??
* Only two $x^n$ terms
* One power of $x$ is double the other.

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