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MrRa [10]
3 years ago
13

Which expression is the factored equivalent of x2 - 5x + 4?

Mathematics
1 answer:
ozzi3 years ago
5 0

Answer:

Step-by-step explanation:

A

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Write a polynomial of degree 5 with zero x=0,i square root 7, -2i
professor190 [17]

Answer:

P(x)=x^5+11x^3+28x

Step-by-step explanation:

<u>Roots of a polynomial</u>

If we know the roots of a polynomial, say x1,x2,x3,...,xn, we can construct the polynomial using the formula

P(x)=a(x-x_1)(x-x_2)(x-x_3)...(x-x_n)

Where a is an arbitrary constant.

We know three of the roots of the degree-5 polynomial are:

x_1=0;\ x_2=\sqrt{7}\boldsymbol{i}:\ x_3=-2\boldsymbol{i}

We can complete the two remaining roots by knowing the complex roots in a polynomial with real coefficients, always come paired with their conjugates. This means that the fourth and fifth roots are:

x_4=-\sqrt{7}\boldsymbol{i}:\ x_3=+2\boldsymbol{i}

Let's build up the polynomial, assuming a=1:

P(x)=(x-0)(x-\sqrt{7}\boldsymbol{i})(x+\sqrt{7}\boldsymbol{i})(x-2\boldsymbol{i})(x+2\boldsymbol{i})

Since:

(a+b\boldsymbol{i})\cdot (a-b\boldsymbol{i})=a^2+b^2

P(x)=(x)(x^2+7)(x^2+4)

Operating the last two factors:

P(x)=(x)(x^4+11x^2+28)

Operating, we have the required polynomial:

\boxed{P(x)=x^5+11x^3+28x}

7 0
3 years ago
CAN SOMEONE HELP ME PLEASE ASAP!?
valentinak56 [21]

Answer:

last option

Step-by-step explanation:

b) 1/6 = 16.7 to 1dp

c) 45% = 45/100 = 9/20

d) 7/9 = 77.8% to 1dp

8 0
3 years ago
For which of these equations is y a function of x?<br><br> y=3x^3<br> xy=1<br> y^2=x<br> y^3=8x
natulia [17]
<span>y is a function of x in y = 3x^3</span>
6 0
4 years ago
1) Jason's football team lost 6 yards from their starting positions and then lost five yards. What number represents a loss of 6
djyliett [7]

Ans: Let it started from zero. And it lasts 6 yards means that -6 represents a loss of 6 yards.

After that, the team lost 5 yards. So, -11 will represent a loss of 5 yards

<span>The team after gaining 12 yards on next day will not be at their starting position. Instead, it will be at ‘1yard’ more than the starting position. The number will be ‘1’ which will represent the position of the team after gaining 12 yards.</span>

8 0
4 years ago
Read 2 more answers
Some number was divided into 42. This quotient was then multiplied by 8,after which the resulting product was added to 10. Given
AURORKA [14]

Answer:

126

Step-by-step explanation:

In order to find the initial number, we need to create the expression that is being mentioned and solve for the initial value by applying the opposite expressions to isolate the variable.

(((x / 42) * 8) + 10) = 34   ... subtract 10 from both sides

((x / 42) * 8) = 24 ... divide both sides by 8

(x / 42) = 3  ... multiply both sides by 42

x = 126

Finally, we can see that the initial value was 126

5 0
3 years ago
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