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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

User Phifi
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1 Answer

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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.

User Kandha
by
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