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erik [133]
3 years ago
13

Write a polynomial of least degree with rational coefficients and with the root -19-5 square root 2.

Mathematics
1 answer:
iogann1982 [59]3 years ago
5 0

Answer:

y = x² + 38x + 311

Step-by-step explanation:

If a polynomial has rational coefficients and irrational roots, then the roots must be conjugate pairs.

y = (x − (-19-5√2)) (x − (-19+5√2))

y = (x + 19+5√2) (x + 19−5√2)

Use FOIL to distribute:

y = x² + x (19−5√2) + x (19+5√2) + (19+5√2)(19−5√2)

y = x² + 19x − 5√2 x + 19x + 5√2 x + (19+5√2)(19−5√2)

y = x² + 38x + (19+5√2)(19−5√2)

Use FOIL to distribute the last term:

y = x² + 38x + 19² − 95√2 + 95√2 − 50

y = x² + 38x + 361 − 50

y = x² + 38x + 311

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Nat2105 [25]

Hey There!

The answer to your problem is x=-3 or x=-4 both answers are correct!

<u>Step 1: Subtract x²+12 from both sides.</u>

−7x−(x²+12)=x²+12−(x²+12)

−x²−7x−12=0

<u>Step 2: Factor left side of equation.</u>

(-x-3)(x+4)=0

<u>Step 3: Set factors equal to 0.</u>

-x-3=0 or x+4=0

<u>Get your answer:</u>

x=-3 or x=-4

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3 years ago
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The sum of two integers is 26. the sum of the squares of the two integers is 340. what is the product of the two numbers?
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Lets say that the two unknown integers are n and m.

We know the following things about n and m:

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And, we want to find nm.

To solve this, we'll use the expansion of the squared of the sum of any two inegers; this is expressed as:

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We can easily solve for nm:

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The answer is 168.

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