Everything Maths Grade 11

CHAPTER 7. SOLVINGQUADRATIC EQUATIONS 7.4

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 = 1

b =− 5

c = 8

Step 3 : Apply the quadratic formula

x =

−b±

√

b^2 − 4 ac

2 a

(7.14)

=

−(−5)±

�

(−5)^2 − 4(1)(8)

2(1)

(7.15)

=

5 ±

√

− 7

2

(7.16)

(7.17)

Step 4 : Write the final answer

Since the expression under the square root is negative these are not real solutions

(

√

− 7 is not a real number). Therefore there are no real solutions to the quadratic

equation x^2 − 5 x + 8 = 0. This means that the graph of the quadratic function

f(x) = x^2 − 5 x + 8 has no x-intercepts, but that theentire graph lies above the

x-axis.

See video: VMezc at http://www.everythingmaths.co.za

Exercise 7 - 3

Solve for t using the quadratic formula.

1. 3 t^2 + t− 4 = 0


2. t^2 − 5 t + 9 = 0


3. 2 t^2 + 6t + 5 = 0


4. 4 t^2 + 2t + 2 = 0

5.− 3 t^2 + 5t− 8 = 0

6.− 5 t^2 + 3t− 3 = 0

7. t^2 − 4 t + 2 = 0