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Temka [501]
2 years ago
6

Please help me fast ​

Mathematics
1 answer:
Andre45 [30]2 years ago
8 0

Answer:

...............................4650

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what is the polynomial function of lowest degree with leading coefficient of 1 and roots 2 and 1 + square root2
Marta_Voda [28]
If the roots to such a polynomial are 2 and 1+\sqrt2, then we can write it as

(x-2)(x-(1+\sqrt2))

courtesy of the fundamental theorem of algebra. Now expanding yields

(x-2)(x-1-\sqrt2)=x^2-2x-(1+\sqrt2)x+2(1+\sqrt2)=x^2-(3+\sqrt2)x+2+2\sqrt2

which would be the correct answer, but clearly this option is not listed. Which is silly, because none of the offered solutions are *the* polynomial of lowest degree and leading coefficient 1.

So this makes me think you're expected to increase the multiplicity of one of the given roots, or you're expected to pull another root out of thin air. Judging by the choices, I think it's the latter, and that you're somehow supposed to know to use 1-\sqrt2 as a root. In this case, that would make our polynomial

(x-2)(x-(1+\sqrt2))(x-(1-\sqrt2))=x^3-4x^2+3x+2

so that the answer is (probably) the third choice.

Whoever originally wrote this question should reevaluate their word choice...
5 0
2 years ago
Negative 10.9p plus 3.9 equals negative 9.18.... what does p equal
Julli [10]

Answer:

-1.2

Step-by-step explanation:

10.9p+3.9=-9.18

Subtract 3.9 from -9.18 to isolate the variable.

10.9p=-13.08

Divide -13.08 by 10.9

-13.08/10.9=-1.2

Which equals

p=-1.2

4 0
3 years ago
Select the correct answer. Simplify the expression below. 4x(3x − 7) − 19x2 A. -7x2 − 7 B. -35x2 C. -7x2 − 28x D. -31x2 − 28x
morpeh [17]

Answer:

C. -7x^2-28x

Step-by-step explanation:

The given expression is 4x(3x-7)-19x^2

We apply the distributive property to expand the parenthesis

12x^2-28x-19x^2

Regroup similar terms to get:

12x^2-19x^2-28x

Combine the similar terms to obtain:

-7x^2-28x

The correct option is C.

5 0
3 years ago
Without a calculator how would you solve this?
mina [271]

Answer:

the largest number that is less than (2+√3)^6 is 2701

Step-by-step explanation:

\bigstar \ (2+\sqrt{3})^6= \\\\C{}^{0}_{6}2^{6}+C{}^{1}_{6}2^{5}\sqrt{3}^1+C{}^{2}_{6}2^{4}\sqrt{3}^2+C{}^{3}_{6}2^{3}\sqrt{3}^3+C{}^{4}_{6}2^{2}\sqrt{3}^4+C{}^{5}_{6}2^{1}\sqrt{3}^5+C{}^{6}_{6}\sqrt{3}^6

=64+192\sqrt{3}+720 +480\sqrt{3} +540+108\sqrt{3} +27\\=1351+780\sqrt{3}

\bigstar\  (2-\sqrt{3} )^6 =\\\\1351-780\sqrt{3}

\bigstar\  \bigstar\  (2+\sqrt{3} )^6+(2-\sqrt{3} )^6 =\\\\1351+780\sqrt{3}+1351-780\sqrt{3}

\Longrightarrow(2+\sqrt{3} )^6+(2-\sqrt{3} )^6 =2702

\Longrightarrow(2+\sqrt{3} )^6 =2702-(2-\sqrt{3} )^6

0 < \left( 2-\sqrt{3} \right) < 1 \Longrightarrow 0 < \left( 2-\sqrt{3} \right)^{6} < 1 \Longrightarrow-1 < \left( 2-\sqrt{3} \right)^{6} < 0

\Longrightarrow2702-1 < 2702-\left( 2-\sqrt{3} \right)^{6} < 2702+0

\Longrightarrow 2701 < \left( 2+\sqrt{3} \right)^{6} < 2702

8 0
2 years ago
S
Scilla [17]

0.03

Step-by-step explanation:

S ∝ t, introduce constant, if value of S depends on t only. Let that constant be 'k'.

=> S = kt

When, S = 0.6 & t = 4:

Answer

=> 0.6 = k(4)

=> 0.6/4 = k

=> 0.15 = k

Therefore, when t = 0.2

=> S = kt

= (0.15)(0.2)

= 0.03

3 0
2 years ago
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