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For which set of values of X is the algebraic expression x^2 - 16 over x^2 -4x - 12 undefined.

For Which Set Of Values Of X Is The Algebraic Expression X2 16 Over X2 4x 12 Undefined class=

Sagot :

Chonccidn

Answer:

Step-by-step explanation:

In order to be undefined, the fraction must have the denominator equal to 0, therefore we need to solve the equation

[tex]x^2 -4x - 12 = 0\\[/tex]

This is a second degree equation, and we can re-write it to

[tex](x-6)(x+2) = 0[/tex]

We notice that the solution to be composed of 2 values:

x = 6

and

x = -2

Therefore the set of values of x for which the said expression is undefined is

S={-2, 6}

Alternatively, if you don't notice how to re-write it factored, you can use the 2nd degree equation solving algorithm:

[tex]\Delta = (-4)^2 - 4\cdot1\cdot(-12) = 16+48 = 64\\x_1 = \frac{-(-4)-\sqrt{64} }{2\cdot1} = -2\\x_1 = \frac{-(-4)+\sqrt{64} }{2\cdot1} = 6[/tex]

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