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mr_godi [17]
2 years ago
11

What is the value of discontinuity of x^2+8x+4/x^2-x-6? Choices:

Mathematics
1 answer:
Morgarella [4.7K]2 years ago
3 0

Answer:

-2

Step-by-step explanation:

Hello,

First of all, let's check the denominator.

x^2-x-6 \ \ \text{ *** How to factorise it ...? ***}\\\\\text{*** The product of the roots is -6=-2*3 and their sum is 1 ***}\\\\x^2-x-6=x^2-3x+2x-6=x(x-3)+2(x-3)=(x+2)(x-3)

Now, let's see the numerator.

x^2+8x+4 \ \text{ *** -2 is not a zero as ***}\\\\(-2)^2+8*(-2)+4=4-16+8=-4\\\\\text{*** 3 is not a zero as ***}\\\\3^2+8*3+4=9+24+4=37\\

So we cannot factorise the numerator with (x+2) or (x-3)

Then, -2 and 3 are the the discontinuities of the expression.

There is only -2 in the list, this is the correct answer.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

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