Question

4. Using the Method of Completing the square, find the zeroes of the following function to the nearest

hundredth.
F(x)=2x^2+12x+5

Answer 1

Given:

The function is:

`F(x)=2x^2+12x+5`

To find:

The zeroes of the given function by using the Method of Completing the square.

Solution:

We have,

`F(x)=2x^2+12x+5`

It can be written as:

`F(x)=2(x^2+6x)+5`

By Method of Completing the square add and subtract square of half of coefficient of x in the parenthesis.

`F(x)=2(x^2+6x+((6)/(2))^2-((6)/(2))^2)+5`

`F(x)=2(x^2+6x+(3)^2)-2(3)^2+5`

`F(x)=2(x+3)^2-2(9)+5`
`[\because (a+b)^2=a^2+2ab+b^2]`

`F(x)=2(x+3)^2-18+5`

`F(x)=2(x+3)^2-13`

For zeroes, F(x)=0.

`2(x+3)^2-13=0`

`2(x+3)^2=13`

`(x+3)^2=(13)/(2)`

`(x+3)^2=6.5`

Taking square root on both sides, we get

`x+3=\pm √(6.5)`

`x=\pm √(6.5)-3`

`x\approx 2.55-3` and
`x\approx -2.55-3`

`x\approx -0.45` and
`x\approx -5.55`

Therefore, the zeroes of the given function are -0.45 and -5.55.