So far most of what we have encountered with quadratics are those for which the coefficient of the $x^2$x2 term is a $1$1. These are called monic quadratics.
A non-monic quadratic is a quadratic that has a coefficient of the $x^2$x2 term not equal to $1$1. Here are some examples of non-monic quadratics:
$3x^2-2x$3x2−2x
$-2x^2+4x-5$−2x2+4x−5
$\frac{x^2}{2}-3x-10$x22−3x−10
$7-1.6x+\sqrt{3}x^2$7−1.6x+√3x2
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 factoring or algebra that is a little more complicated. Methods that are particularly suited to non-monic quadratics are covered in non-monic factoring.
Examples
Question 1
Solve for $x$x: $11x^2=7x$11x2=7x Write all solutions on the same line, separated by commas.
Question 2
Solve the following equation by first factoring the left hand side of the equation. $5x^2+22x+8=0$5x2+22x+8=0 Write all solutions on the same line, separated by commas.
Question 3
Solve the following equation for $b$b using the Factor By Grouping Method of factoring: $15-11b-12b^2=0$15−11b−12b2=0 Write all solutions in fraction form, on the same line separated by commas.