Question

f(x)=x^2+4x-6 a) f(x) can be written in the form (x+m)^2+n find the value of m and the value of n b) use your answer to part (a) to find the positive solution to x^2+4x-6=0

Answer 1

see explanation

Explanation:

Using the method of completing the square.

Given

f(x) = x² + 4x - 6

add/subtract ( half the coefficient of the x- term )² to x² + 4x

f(x) = x² + 2(2)x 6 + 4 - 4 - 6

= (x + 2)² - 10

with m = 2 and n = - 10

To solve the equation let f(x) = 0 , that is

(x + 2)² - 10 = 0 ( add 10 to both sides )

(x + 2)² = 10 ( take the square root of both sides )

x + 2 = ±
`√(10)` ( subtract 2 from both sides )

x = - 2 ±
`√(10)`

The positive solution is

x = - 2+
`√(10)` ≈ 1.16 ( to 2 dec. places )