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2 years ago

For what value of k,is the polynomial p(x)= 3x4 – 9x3 + x2 - 15x + k completely divisible by 3x2 - 5

Mathematics

1 answer:

masha68 [24]2 years ago

6 0

Answer:

k = -10

Step-by-step explanation:

$p(x)=3x^{4} - 9x^{3} + x^{2} + 15x + k\\3x^{2} (x^{2} -3x + y) -5 (x^{2} -3x + y)$

When we expand the above

$p(x)=3x^{4} - 9x^{3} + 3x^{2}y- 5x^{2} + 15x - 5y$

When we take consider $x^{2}$ with the original expression

3y - 5 = 1

3y = 6 ⇒ y = 2

k = -5y ⇒ k = -10

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2 years ago

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2 years ago

The graph shows the solution to the initial value problem y'(t)=mt, y(t0)= -4

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$y'(t)=mt
\\
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$y=at^2+b
\\
\\3=a\times 2^2-2
\\
\\3=4a-2
\\
\\5=4a
\\
\\a= \frac{5}{4} 
\\
\\y=\frac{5}{4} t^2-2 \\ \\y= \frac{m}{2} t^2+C
\\ \\ \frac{m}{2} = \frac{5}{4} 
\\
\\m= \frac{5}{2} 
\\
\\C=-2
\\
\\y(t_0)=-4
\\
\\-4= \frac{5}{4} t_0^2-2
\\
\\ -2= \frac{5}{4} t_0^2
\\
\\ t_0^2=- \frac{8}{5} 
\\
\\t_0=\pm \sqrt{- \frac{8}{5} }$

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2 years ago

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Step-by-step explanation:

sample response

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2 years ago

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For what value of k,is the polynomial p(x)= 3x4 – 9x3 + x2 - 15x + k completely divisible by 3x2 - 5​

For what value of k,is the polynomial p(x)= 3x4 – 9x3 + x2 - 15x + k completely divisible by 3x2 - 5