Quadratic Equations

Lesson

So far most of what we have encountered with quadratics are those for which the coefficient of the $x^2$`x`2 term is a $1$1. These are called monic quadratics.

A non-monic quadratic is a quadratic that has a coefficient of the $x^2$`x`2 term not equal to $1$1. Here are some examples of non-monic quadratics:

$3x^2-2x$3`x`2−2`x`

$-2x^2+4x-5$−2`x`2+4`x`−5

$\frac{x^2}{2}-3x-10$`x`22−3`x`−10

$7-1.6x+\sqrt{3}x^2$7−1.6`x`+√3`x`2

We can use all the methods we have already seen to solve non-monic quadratic equations. The only difference is that some non-monic quadratics involve factorising or algebra that is a little more complicated. Methods that are particularly suited to non-monic quadratics are covered in non-monic factorisation.

**
Solve for $x$ x:**

$11x^2=7x$11`x`2=7`x`

**Write all solutions on the same line, separated by commas.**

**Solve the following equation by first factorising the left hand side of the equation. **

$5x^2+22x+8=0$5`x`2+22`x`+8=0

**Write all solutions on the same line, separated by commas.**

**Solve the following equation for $b$ b using the PSF method of factorisation: $15-11b-12b^2=0$15−11b−12b2=0**

**Write all solutions in fraction form, on the same line separated by commas.**