Everything Maths Grade 10

Worked example 5: Solving quadratic equations

QUESTION

Find the roots:

0 = 2 x^2 + 4x 2

SOLUTION

Step 1: The equation is already in the required form,ax^2 +bx+c= 0

Step 2: Divide the equation by common factor 2

 2 x^2 + 4x2 = 0

x^2  2 x+ 1 = 0

Step 3: Factorise

(x1) (x1) = 0

(x1)^2 = 0

Step 4: The quadratic is a perfect square

This is an example of a special situation in which there is only one solution to the quadratic equation because
both factors are the same.

x1 = 0

)x= 1

Step 5: Check the answer by substituting back into the original equation

Step 6: Write final answer

The solution to0 = 2 x^2 + 4x 2 isx= 1.

Exercise 4 – 2:

1.Write the following in standard form:

a) (r+ 4)(5r4) = 16 b)(3r8)(2r3) = 15 c) (d+ 5)(2d+ 5) = 8

2.Solve the following equations:

a) x^2 + 2x15 = 0 b)p^2  7 p18 = 0

c) 9 x^2  6 x8 = 0 d) 5 x^2 + 21x54 = 0

e) 4 z^2 + 12z+ 8 = 0 f)b^2 + 7b12 = 0

g)  3 a^2 + 27a54 = 0 h) 4 y^2 9 = 0

80 4.3. Solving quadratic equations