Class X

Non-monic quadratic equations

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$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 factorising or algebra that is a little more complicated. Methods that are particularly suited to non-monic quadratics are covered in non-monic factorisation.

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 factorising 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 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.

Outcomes

10.A.QE.1

Standard form of a quadratic equation ax^2 + bx + c = 0, (a ≠0). Solution of quadratic equations (only real roots) by factorization and by completing the square, i.e., by using quadratic formula. Relationship between discriminant and nature of roots. Problems related to day-to-day activities to be incorporated