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anonymous
 one year ago
Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.
4, 2, and 1 + 2i
How would I solve this?
anonymous
 one year ago
Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. 4, 2, and 1 + 2i How would I solve this?

This Question is Closed

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.0so the polynomial has 4 roots.. the real roots are x = 4 and x = 2 the complex roots are \[x = 1 \pm i\]

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.0so to find the complex roots start with \[x = 1 \pm i\] add 1 to both sides \[x + 1 = \pm i\] square both sides of the equation \[(x + 1)^2 = i^2\] remember i^2 = 1 then \[x^2 + 2x + 1 = 1\] add 1 to both sides of the equation and you will have the quadratic factor of the polynomial... so the polynomial is \[P(x) = (x^2 + 2x +1)(x 4)(x+1)\] just distribute for the equation

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.0is that another question...?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0No, is that the correct answers @campbell_st

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.0well the polynomial is \[P(x) = (x^2 + 2x + 2)(x 4)(x +2)\] which becomes \[P(x) = (x^2+ 2x +2)(x^2 2x  8)\] you just need to multiply the 2 quadratic factors together

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The answer I come up with is not one of the options. X^410x^220x16

Mertsj
 one year ago
Best ResponseYou've already chosen the best response.1f(x)=(x4)(x+2)[x(1+2i)][x(12i)]

Mertsj
 one year ago
Best ResponseYou've already chosen the best response.1Multiply the four factors and that will be your answer.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay I got x^4+6.5x^226x

Mertsj
 one year ago
Best ResponseYou've already chosen the best response.1f(x)=(x^22x8)(x^2+5)=x^42x^38x^2+5x^210x40=x^42x^33x^210x40

Mertsj
 one year ago
Best ResponseYou've already chosen the best response.1That's what I get from multiplying those 4 factors. Is that one of your choices?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes, I must have done it wrong. Thank you.

Mertsj
 one year ago
Best ResponseYou've already chosen the best response.1If 4is a root, then x4 is a factor. If 2 is a root then x(2)=x+2 is a factor If 1+2i is a root then 1  2i is also a root If 1+2i is a root then x(1+2i) is a factor If 12i is a root then x  (12i) is a factor

Mertsj
 one year ago
Best ResponseYou've already chosen the best response.1So now we have 4 factors of the polynomial: (x4)(x+2)[x(1+2i)][x(12i)] (x4)(x+2)=x^22x8 [x(1+2i)][x(12i)]=x^2x(12i)x(1+2i)+(1+2i)(12i)= x^2+x+2xi+x2xi+5=x^2+2x+5

Mertsj
 one year ago
Best ResponseYou've already chosen the best response.1So now we must multiply (x^22x+8)(x^2+2x+5)= x^4+2x^3+5x^22x^34x^210x+8x^2+16x+40= x^4+9x^2+6x+40

Mertsj
 one year ago
Best ResponseYou've already chosen the best response.1Is that one of your choices?

Mertsj
 one year ago
Best ResponseYou've already chosen the best response.1What are the answer choices?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0a. f(x) = x4  7x2  26x  40 b. f(x) = x4  3x3  8x2  13x  40 c. f(x) = x4 + 6.5x2  26x  40 d. f(x) = x4  3x3 + 8x2 + 13x + 40

Mertsj
 one year ago
Best ResponseYou've already chosen the best response.1I made a typo when I multiplied: (x^22x8)(x^2+2x+5)=x^4+2x^3+5x^22x^34x^210x8x^216x40= x^47x^226x40

Mertsj
 one year ago
Best ResponseYou've already chosen the best response.1Before I used x^22x+8 instead of x^22x8
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