Everything Maths Grade 11

CHAPTER 7. SOLVINGQUADRATIC EQUATIONS 7.2

a^2 − 3 a− 10 = 0

Step 2 : Factorise the trinomial

(a + 2)(a− 5) = 0

Step 3 : Solve the equation

a + 2 = 0

or

a− 5 = 0

Solve the two linear equations and check the solutions in the original equation.

Step 4 : Write the final answer

Therefore, a =− 2 or a = 5

Example 3: Solving fractions that lead to a quadratic equation

QUESTION

Solve for b:b^3 +2b+ 1 =b+1^4

SOLUTION

Step 1 : Multiply both sides over the lowest common denominator

3 b(b + 1) + (b + 2)(b + 1)

(b + 2)(b + 1)

=

4(b + 2)

(b + 2)(b + 1)

Step 2 : Determine the restrictions

The restrictions are the values for b that would result in thedenominator being 0.

Since a denominator of 0 would make the fraction undefined, b cannot be these

values. Therefore, b�=− 2 and b�=− 1

Step 3 : Simplify equation to the standard form

The denominators on both sides of the equation are equal. This means we can

drop them (by multiplying both sides of the equation by (b + 2)(b + 1)) and just

work with the numerators.

3 b^2 + 3b + b^2 + 3b + 2 = 4b + 8

4 b^2 + 2b− 6 = 0

2 b^2 + b− 3 = 0

Step 4 : Factorise the trinomialand solve the equation