A number was multiplied by 6 then increased by 3 and the result was 33

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

2 years ago

Given that x is a normally distributed random variable with a mean of 50 and a standard deviation of 2, find the probability tha

Shkiper50 [21]

Let X be the normal variable with mean μ =50 and standard deviation σ =2

We have to find probability that x is between 47 and 54

P(47 < X < 54) = P(X < 54) - P(X < 47)

= $P(\frac{x-mean}{standard deviation}$ - $P(\frac{x-mean}{standard deviation}$

= P(Z < 2) - P(Z < -1.5)

Using standard normal z score table to find probabilities we get

P(Z < 2) = 0.9772

P(Z < -1.5) = 0.0668

P(47 < X < 54) = P(Z < 2) - P(Z < -1.5)

= 0.9772 - 0.0668

P(47 < X < 54) = 0.9104

The probability that x is between 47 and 54 is 0.9104

5 0

2 years ago

NEED ANSWER FAST 11 POINTS!!!

AleksandrR [38]

Option 2 is your answer

Your numbers on the left are going across. Then the numbers on the top are going down

5 0

2 years ago

Mike took a taxi from his home to the airport. The taxi driver charged an initial fee of $6 plus $3 per mile. The total fare was

snow_tiger [21]

Answer:

x=6

Step-by-step explanation:

Put the problem into y=mx+b format we knoe the inital value b is 6 now m is 3 and y the overall price is 24. Use the distributive property.

24=6+3x y=6+3x y=24

-6 -6

18=3x

3 3

6=x

x=6

8 0

2 years ago

Read 2 more answers

A train goes at a constant speed. If it covers 150 miles in 2 1/2 hours What distance would it cover in 3 hours?

Hoochie [10]

Hi there!

In order to find your answer, you'll need to use the cross product method :

150 miles → 2 1/2 hours = 150 minutes

x miles → 3 hours = 180 minutes

(150 × 180) ÷ 150 = x miles

27,000 ÷ 150 = x miles

180 = x miles

Your answer is: A train would cover 180 miles in 3 hours.

There you go! I really hope this helped, if there's anything just let me know! :)

8 0

2 years ago

Read 2 more answers