Who wants 10 points for some math help?

Question

Find one ordered pair solution for the equation below, when x=2.

f(x)=2x3+x2-10x-5

Given a zero: x=2, of the polynomial: x3-4x2+21x-34=0, find the others.

Answer 1

f(x) =2(2)^3 + 2^2 -10(2) -5 = 16 + 4 - 20 - 5 = -5
(2,-5)

Synthetic division:
2 1 -4 21 -34
2 -4 34
1 -2 17 0
x^2-2x+17
Use the quadratic formula

x =(2±sqrt(4-68))/2
x =(2±8i)/2
x = 1±4i

Answer 2

I'm not going to do this problem for you because it is simple and you will probably have to know how to do it in the future. To find an ordered pair solution for an equation when you are given x=2:

First subsitute 2 in for x in the equation. Then solve. Your answer will be the y coordinate. Then the ordered pair solution is (2,y).

To find the zeros of a polynomial:

First factor the polynomial. Set each factor equal to zero. Solve for x.

Answer 3

i)

f(x) = 2x^3 + x^2 - 10x - 5

f(2) = 2(2)^3 + (2)^2 - 10(2) - 5

f(2) = 16 + 4 - 20 - 5 = -5

one ordered pair of solution is (2,-5)

ii)

Since x = 2 is one of the zeros, x-2 is a factor of P(x)

Divide P(x) by x - 2 synthetically to get quadratic equation which upon solving will give remaining two zeros.

x-2)x^3-4x^2+21x-34(x^2
......x^3-2x^2
_______________
.............-2x^2+21x(-2x
.............-2x^2+4x
_________________
.....................+17x-34(17
.....................+17x-34
____________________
...........................0

so the quotient is x^2 - 2x + 17

x^2 - 2x + 17

using quadratic formula

x = [2 +/- sqrt(4 - 68)] / 2

x = 2 +/- sqrt(-64)] / 2

x = [2 +/- 8i] / 2

x = 1 +/- 4i

So three zeros of polynomial are 2, (1 + 4i) and (1 - 4i)

Answer 4

f(2) = 2*2^3 +2^2 -10*2-5 = 16+4 - 20 -5 = -5
So ordered pair is (2,-5)

Divide by x-2 getting x^2-2x+17
x = [2 +/- sqrt(2^2 - 4(1)(17))]/2
x = [2 +/- sqrt(-64)]/2
x = [2 +/- 8i]/2
x = 1 +/- 4i

Answer 5

yeah 2 points is good enough for me as well... those homework packets can be real stinkers... glad I'm out of school.