2022-01-17
Answered

How can you determine all of the zeroes (real and imaginary) of the polynomial function:

$P\left(x\right)={x}^{4}+2{x}^{3}-9{x}^{2}-10x-24?$

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nick1337

Answered 2022-01-17
Author has **510** answers

Step 1

You can expect any factors to divide -24, the constant term over the lead coefficient. So check 1, 2, 3, 4, 6,12, 24 and their negatives. Turns out that 3 and -4 work, so you are down to a quadratic

so the roots are

star233

Answered 2022-01-17
Author has **137** answers

Step 1

The basic trick is to try finding 3 numbers k,m,n which would enable us to write:

that is:

The basic trick is to try finding 3 numbers k,m,n which would enable us to write:

Rearrange these equations and get

From the 2 equations on the left we get

and therefore one possible solution would be:

Hence we get the following factorization of the given polynomial:

So, all the problem has now been reduced into finding the 4 roots of the 2 quadratic polynomials, which are

and

asked 2022-03-17

a) What is the sum of: $(3-4i)$ and $(-21-6i)$ ?

1)$-24-10i$

2)$18-2i$

3)$-18-10i$

4)$24+2i$

b) Simplify$\frac{2-3i}{2+2i}$

1)$-\frac{1}{24};\text{}-\left(\frac{5}{4}\right)i$

2)$-\frac{1}{24};\text{}+\left(\frac{5}{4}\right)i$

3)$\frac{1}{22};\text{}-\frac{1}{22};\text{}i$

4)$\frac{1}{22};\text{}+\frac{1}{22};i$

1)

2)

3)

4)

b) Simplify

1)

2)

3)

4)

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What are complex numbers? $\mathrm{ln}(1-i)$

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Find the product $z}_{1}{z}_{2$ and the quotient $\frac{{z}_{1}}{{z}_{2}}$ . Express your answers in polar form.

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${z}_{1}{z}_{2}=?$

$\frac{{z}_{1}}{{z}_{2}}=?$

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Multiplicative Inverse of a Complex Number
The multiplicative inverse of a complex number z is
a complex number zm such that $z\times zm=1$ . Find the
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$z=1+i$