Question

Solve the following quadratic equation:

x² + 4x – 8 = 0

Give your Solution correct to one decimal place.

(Use mathematical tables if necessary.)

Answer 1

Given: x² + 4x – 8 = 0

Here a = 1, b = 4, c = – 8

D = b² – 4ac

= (4)² – 4 × 1 × (– 8)

= 16 + 32

= 48 > 0

∴ Roots are real.

So, x = `(-b ± sqrt(D))/(2a)`

x = `(-4 ± sqrt(48))/(2 xx 1)`

= `(-4 ± 4sqrt(3))/2`

= `-2 ± 2sqrt(3)`

x = `-2 ± (2 xx 1.73)`   ...`{∵ sqrt(3) = 1.73}` 

= – 2 ± 3.46

`\implies` x = 1.46, – 5.46

or x = 1.5, – 5.5   ...(Correct to one decimal place)