For anyone who is a genius at math?

Question

-4 is a zero of the polynomial x^3-2x^2-11x+52, what are all the other zeros?

Answer 1

Since -4 is a root, (x + 4) is a factor of the polynomial.
Therefore, if we divide by x + 4 we will get a quadratic polynomial that you can solve by factoring or using the quadratic formula.

x² - 6x + 13
_________________
x + 4 | x³ - 2x² -11x + 52
. x³ + 4x²
. -6x² - 11x
. -6x² - 24x
. 13x + 52
. 13x + 52
. 0

Now you have the quadratic x² -6x + 13. You have to use the quadratic formula since it doesn't factor.

x = (-b ± √{b² - 4ac}) ÷ 2a

x = [6 ± √{6² - 4(1)(13)}] ÷ 2(1)
= [6 ± √{36 - 52}] ÷ 2
= [6 ± √{-16} ] ÷ 2
= [6 ± 4i ] ÷ 2
= 3 ± 2i

Therefore, the roots of the polynomial x³ - 2x² -11x + 52 are:
x = -4, 3+2i, 3-2i

Answer 2

If f(-4) = 0 then x + 4 is a factor

So x³ - 2x² - 11x + 52 = (x + 4)(x² - 6x + 13)

So other zeros are solution to x² - 6x + 13 = 0

By quadratic formula, these are ½{6 ± √(-16)}

ie 3 ± 2i where i² = -1

Answer 3

Using synthetic division, you get
x^3 - 2x^2 - 11x + 52 = (x+4)(x^2 - 6x + 13)
Which is a quadratic equation.
If we calculate the discriminant, we get
b^2 - 4ac = (-6)^2 - 4(1)(13) = 36 - 52 = -16
So we have no other REAL zeros, but we do have the complex zeros of
(6 + 4i)/2 and (6 - 4i)/2 = 3 + 2i and 3 - 2i

Answer 4

Hint: If -4 is a zero, x +4 is a factor. Divide x^3-2x^2-11x+52
by x + 4, set the remaining factor to 0 and solve
the resulting quadratic.

Answer 5

This is getting into complex numbers, but...the other answers are:

x = 3 + 2i
x = 3 - 2i
x = -4

Where
i = sqrt(-1)
i^2 = -1

If you try dividing your polynomial by (x+4) , you end up with the polynomial: x^2 - 6x + 13, which NEVER touches the x axis, therefore it never equals zero when discussing real numbers.

However, if you take x^2 - 6x + 13 and put it into the quadratic formula:

x = [-(-6) +/- sqrt( (-6)^2 - 4*1*13 )]/2*1
x = [6 +/- sqrt(36 - 52)]/2
x = 3 +/- sqrt(-16)/2
x = 3 +/- sqrt(-2)
x = 3 +/- 2i

That is how you get x = 3 - 2i and x = 3 + 2i

Answer 6

Divide the polynom by (x + 4). You will get a second degree polynom that you can solve with the quadratic equation.

Answer 7

copy and paste copy and paste LOL

Answer 8

use synthetic division

Answer 9

LOL I'M A NERD NOT A GENIOUS...JUST THINKING BOUT IT GAVE ME A HEADACHE. HAHA