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snow_lady [41]
3 years ago
12

What multiples to 42 and adds to -2

Mathematics
1 answer:
solniwko [45]3 years ago
4 0

Answer:

Step-by-step explanation:

xy = 42

x+y = - 2                   Substitute into the top equation

y = -2 - x                   Put in for y

x(-2 - x) = 42             Remove the brackets

-2x - x^2 = 42           Subtract 42 from both sides.

-2x - x^2 - 42 = 0      Put in the more normal order.

-x^2 - 2x - 42 = 0      Multiply by -1

x^2 + 2x + 42 = 0

This cannot be factored. It gives complex roots as it is written. I will give you the answer but I kind of doubt the question is correct.

x1 = - 1 + 6.40i

x2 = -1 - 6.40i

Leave a comment if you have a correction.

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ANSWER

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EXPLANATION

The given rational function is

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We need to rationalize the denominator by multiplying both the numerator and the denominator by the conjugate of

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When we rationalize we obtain:

\frac{5( \sqrt{11}  +  \sqrt{3} )}{(\sqrt{11}  - \sqrt{3} )( \sqrt{11}  +  \sqrt{3} )}

The denominator is now a difference of two squares:

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\frac{5( \sqrt{11}  +  \sqrt{3} )}{( \sqrt{11}) ^{2}    -  ( \sqrt{3}) ^{2}  )}

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\frac{5( \sqrt{11}  +  \sqrt{3} )} {8}

Or

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