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4 years ago

Find the GCF of the numbers using prime factorizations for 4, 10 5, 11 6, 8 14, 42 45, 63 60, 90

Mathematics

1 answer:

irinina [24]4 years ago

3 0

8 Is the awnser your welcome

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Write the equation of a polynomial of degree 3, with zeros 1, 2 and -1 where f(0)=2

drek231 [11]

Answer:

The equation of a polynomial of degree 3, with zeros 1, 2 and -1 is $x^{3}-2 x^{2}-x+2=0$

Solution:

Given, the polynomial has degree 3 and roots as 1, 2, and -1. And f(0) = 2.

We have to find the equation of the above polynomial.

We know that, general equation of 3rd degree polynomial is

$F(x)=x^{3}-(a+b+c) x^{2}+(a b+b c+a c) x-a b c=0$

where a, b, c are roots of the polynomial.

Here in our problem, a = 1, b = 2, c = -1.

Substitute the above values in f(x)

$F(x)=x^{3}-(1+2+(-1)) x^{2}+(1 \times 2+2(-1)+1(-1)) x-1 \times 2 \times(-1)=0$

$\begin{array}{l}{\rightarrow x^{3}-(3-1) x^{2}+(2-2-1) x-(-2)=0} \\ {\rightarrow x^{3}-(2) x^{2}+(-1) x-(-2)=0} \\ {\rightarrow x^{3}-2 x^{2}-x+2=0}\end{array}$

So, the equation is $x^{3}-2 x^{2}-x+2=0$

Let us put x = 0 in f(x) to check whether our answer is correct or not.

$\mathrm{F}(0) \rightarrow 0^{3}-2(0)^{2}-0+2=2$

Hence, the equation of the polynomial is $x^{3}-2 x^{2}-x+2=0$

3 0

3 years ago

Simplify (x -3)(x + 7) using the table method, and identify the resulting

xxTIMURxx [149]

(x-3)(x+7) —> multiply them together I do it by FOIL which stands for Firsts Inners Outers Lasts

x’(squared)+7x-3x-21 —> simplify

x(squared)+4x-21

4 0

3 years ago

Read 2 more answers

3+2×(8-5)+6 please answer if you answer I will follow if it is right

amid [387]

Answer: 3+2×(8-5)+6 =15

7 0

3 years ago

Read 2 more answers

What is the area of the base of the cone below? Round the number to the nearest tenth if necessary.

Svetach [21]

Answer:

19.5

Step-by-step explanation:

8 0

3 years ago

What are the lateral area and the surface of the cone shown below?

Ierofanga [76]

$\bf \textit{lateral surface area of a cone}\\\\
LA=\pi r\stackrel{slant~height}{\sqrt{r^2+h^2}}~~
\begin{cases}
r=radius\\
h=height\\
-------\\
r=11\\
\stackrel{slant~height}{\sqrt{r^2+h^2}}=24
\end{cases}\implies LA=\pi (11)(24)
\\\\\\
\boxed{LA=264\pi }\\\\
-------------------------------$

$\bf \textit{total surface area of a cone}\\\\
SA=\pi r\stackrel{slant~height}{\sqrt{r^2+h^2}}+\pi r^2~~
\begin{cases}
r=radius\\
h=height\\
-------\\
r=11\\
\stackrel{slant~height}{\sqrt{r^2+h^2}}=24
\end{cases}
\\\\\\
SA=\pi (11)(24)+\pi (11)^2\implies SA=264\pi +121\pi 
\\\\\\
\boxed{SA=385\pi }$

3 0

3 years ago