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4vir4ik [10]
2 years ago
9

Which polynomial function has a leading coefficient of 1 and roots (7 i) and (5 – i) with multiplicity 1? f(x) = (x 7)(x – i)(x

5)(x i) f(x) = (x – 7)(x – i)(x – 5)(x i) f(x) = (x – (7 – i))(x – (5 i))(x – (7 i))(x – (5 – i)) f(x) = (x (7 – i))(x (5 i))(x (7 i))(x (5 – i))
Mathematics
1 answer:
Nuetrik [128]2 years ago
5 0

It looks like you might have intended to say the roots are 7 + i and 5 - i, judging by the extra space between 7 and i.

The simplest polynomial with these characteristics would be

f(x) = (x - (7 + i)) (x - (5 - i))

but seeing as each of the options appears to be a quartic polynomial, I suspect f(x) is also supposed to have only real coefficients. In that case, we need to pair up any complex root with its conjugate to "complete" f(x). We end up with

f(x) = (x - (7 + i)) (x - (7 - i)) (x - (5 - i)) (x - (5 + i))

which appears to most closely resemble the third option. Upon expanding, we see f(x) does indeed have real coefficients:

f(x) = (x^2 - (7^2 - i^2)) (x^2 - (5^2 - i^2)) = (x^2 - 8) (x^2 - 6) = x^4 - 14x^2 + 48

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mihalych1998 [28]

Answer:

ΔLMN ≅ ΔLQP by (SAA)

Step-by-step explanation:

It is given that line (NM) is congruent to the line (PQ), meaning they have the same measure. This is signified by the small red line on each of these sides.

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Finally one can figure out that angle (NLM) is congruent to angle (PLQ) by the vertical angles theorem. The verticle angles theorem states that when two lines intersect, the opposite angles are congruent.

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6 0
2 years ago
What is the value of x ? 6.75 + 3/8x = 13 1/4
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Let's solve your equation step-by-step.

6.75+38x=1314

Step 1: Simplify both sides of the equation.

38x+6.75=534

Step 2: Subtract 6.75 from both sides.

38x+6.75−6.75=534−6.75

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Step 3: Multiply both sides by 8/3.

(83)*(38x)=(83)*(132)

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Answer:

x=1713

7 0
3 years ago
What is the value of x in a 30-60-90 triangle with a hypotenuse of x+12 and a longer side of x?
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I don't think I made a mistake, but it is sure possible.Check the numbers and my method. 
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anzhelika [568]

No it does not stay the same

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4 0
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