topic badge
CanadaON
Grade 12

Quadratic equations (a not 1)

Lesson

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$3x22x

$-2x^2+4x-5$2x2+4x5

$\frac{x^2}{2}-3x-10$x223x10

$7-1.6x+\sqrt{3}x^2$71.6x+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

  1. 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

  1. 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$1511b12b2=0

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

Outcomes

12CT.B.3.1

Solve polynomial equations in one variable, of degree no higher than four (e.g., x^2 – 4x = 0, x^4 – 16 = 0, 3x^2 + 5x + 2 = 0), by selecting and applying strategies (i.e., common factoring; difference of squares; trinomial factoring), and verify solutions using technology

What is Mathspace

About Mathspace