Find a polynomial equation with real coefficients that has the given roots.
5 and -7i
Write a polynomial equation with roots 5 and -7i
x^3 - __ x^2 + __ x -__ = 0
Don't know if they still teach that, but ....
for any quadratic equation of the form
ax^2 + bx + c = 0
the sum of the roots is -b/a , and the product of the roots is c/a
complex roots always appear as conjugate pairs, so they must be
5-7i and 5+7i
sum = 10
product = (5-7u)(5+7i) = 25 - 49i^2 = 25+49 = 74
equation must be
x^2 - 10x + 74 = 0
or .... if the roots are 5-7i and 5+7i
then (x - (5-7i))(x - (5+7i)) = 0
(x - 5 + 7i)(x - 5 - 7i) = 0
x^2 - 5x - 7ix - 5x + 25 + 35i + 7ix - 35i - 49i^2 = 0
x^2 - 10x + 25 - 49i^2 = 0 , but i^2 = -1
x^2 - 10x + 74 = 0
Answer this Question
Use the rational root theorem to list all possible rational roots for the equation. X^3+2x-9=0. Use the rational root theorem to list all possible rational roots for the equation. 3X^3+9x-6=0. A polynomial function P(x) with rational coefficients has the
- asked by Chelsey
- 13,599 views
Find a polynomial with integer coefficients that satisfies the given conditions. P has degree 2 and zeros 2 + i and 2 − i.
- asked by Drue
- 1,802 views
The function f is defined by f(x)=2x^2-6x+5 Find the set of values of p for which the equation f(x)=p has no real roots. Thanks in advance!
- asked by Audrey
- 4,816 views
ALGEBRA CHECK ANSWERS
Solve each equation by graphing the related function. If the equation has no real-number solution, write no solution. NOTE: when I write + it has a minus on the bottom too x^2+7=0 a. x= +7 b. x = +3.5 c. x= 0 d. no solution *** 3x^2=0 a. +3 b. +1/3 c. 0
- asked by a
- 24,139 views
Q: Write a quadratic equation with integral coefficients whose roots are -6+i and -6-i My Answer: x^2+12x+37 (first) sum=-12 product=37 (then) write equation using formula x^2-(sum)x+product Is my work and answer correct?
- asked by Bryan
- 989 views
the roots of 2x^2 - 3x = 4 are a and b. find the simplest quadratic equation which has roots 1/a and 1/b
- asked by isha
- 2,829 views
A polynomial function f(x) with real coefficients has the given degree, zeros, and solution point. Degree: 3 Zeros: -2,2+2√2i Solution Point: f(−1) = −68 (a) Write the function in completely factored form. (b) Write the function in polynomial form.
- asked by Ben Dover III
- 4,473 views
Fine a third degree polynomial function f(x) with real coefficients that has 4 and 2i are zeros and such that f(-1) =-50 4 21 -2i (x-4)(x-2i)(x+2i) (x-4)(x2+4) x3-16+4x-4x2 (x3-4x2+4x-16) -50=a(-1-4-4-16) -50=.25 a=2 Not understanding, please help
- asked by Sally
- 1,151 views
What are the real and complex solutions of the polynomial equation? x^4 - 41x^2 = -400
- asked by |-/
- 3,500 views
An equation with real coefficients has 1-i, 3 and 4 among it's roots. What is the lowest possible degree of the equations?
- asked by KJ
- 1,191 views
Write a polynomial function of minimum degree in standard form with real coefficients whose zeros and their multiplicities include those listed. 2(multiplicity 2), -4(multiplicity 3)
- asked by Anonymous
- 1,321 views
Find a degree 3 polynomial with real coefficients having zeros 2 and 4-3i and a lead coefficient of 1.
- asked by gigi
- 1,246 views
Find a polynomial function P of the lowest possible degree, having real coefficients, a leading coefficient of 1, and with the given zeros. 2plus2i, minus1, and 2
- asked by Peter Asiedu
- 1,762 views
For what value of k does the equation x2 + kx + 9have: Two distinct real roots One real root No real root
- asked by A
- 3,600 views
Determine the real roots of the equation: (5x^2 + 20)(3x^2 - 48) = 0
- asked by Labz
- 575 views
Write a quartic funciton that has 2 real and 2 imaginary roots and rewrite the polynomialin standard form.
- asked by Piggy
- 899 views
find a 4th degree polynomial with integer coefficients that has zeros 3i and -1 with -1 a zero of multiplicity 2
- asked by Rose
- 381 views
Find a polynomial with integer coefficients that satisfies the given conditions. R has degree 4 and zeros 3 − 4i and 5, with 5 a zero of multiplicity 2.
- asked by Kyle
- 2,448 views
a polynomial equation with rational coefficients has the roots 7+sgrt3, 2-sgrt6 find two additional roots 7-sgrt3, 2+sgrt6 3-sgrt7, 6+sgrt2 7+sgrt3, 2-sgrt6 3+sgrt7, 6=sgrt2 could someone help
- asked by lee
- 7,601 views
Form a polynomial f(x) with real coefficients, with leading coefficient 1, having the given degree and zeros. Degree: 4; zeros: -4+3i and 1; multiplicity of 2
- asked by Sam
- 1,874 views