Everything Maths Grade 11

7.4 CHAPTER 7. SOLVINGQUADRATIC EQUATIONS

Example 6: Using the quadratic formula

QUESTION

Find the roots of the function f(x) = 2x^2 + 3x− 7.

SOLUTION

Step 1 : Determine whether theequation can be factorised

The expression cannotbe factorised. Therefore, the general quadraticformula

must be used.

Step 2 : Identify the coefficients in the equation for usein the formula

From the equation:

a = 2

b = 3

c =− 7

Step 3 : Apply the quadratic formula

Always write down the formula first and then substitute the values of a, b and c.

x =

−b±

√

b^2 − 4 ac

2 a

(7.10)

=

−(3)±

�

(3)^2 − 4(2)(−7)

2(2)

(7.11)

=

− 3 ±

√

65

4

(7.12)

=

− 3 ±

√

65

4

(7.13)

Step 4 : Write the final answer

The two roots of f(x) = 2x^2 + 3x− 7 are x =−3+

√

65

4 and

− 3 −

√

65

4.

Example 7: Using the quadratic formula but no solution

QUESTION

Find the solutions to thequadratic equation x^2 − 5 x + 8 = 0.