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

Question

asked May 8, 2022 5.6k views

1 Answer

Kandha · Answer 1 · 2022-05-14T03:38:47+0000

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.