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.

$F(x)=2(x^2+6x+(\dfrac{6}{2})^2-(\dfrac{6}{2})^2)+5$

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

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

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

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

For zeroes, F(x)=0.

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

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

$(x+3)^2=\dfrac{13}{2}$

$(x+3)^2=6.5$

Taking square root on both sides, we get

$x+3=\pm \sqrt{6.5}$

$x=\pm \sqrt{6.5}-3$

$x\approx 2.55-3$ 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.