Polynomial equation with real coefficients that has roots -1, 4 - 2i is x^3 - 7x^2 + 12x + 20 = 0.

Cheyanne Leigh 2021-01-19 Answered

Polynomial equation with real coefficients that has roots 1,42i is x37x2+12x+20=0.

You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

broliY
Answered 2021-01-20 Author has 97 answers
Given:) 1,42i
Used Formula:
(a+b)(ab)=a2b2
Calculation:
If the polynomial has real coefficients, then it’s imaginary roots occur in conjugate pairs. So, a polynomial with the given root 4 — 2i must have another root as 4 + 2i.
Since each root of the equation corresponds to a factor of the polynomial also the roots indicate zeros of that polynomial.
Hence, below mentioned equation is written as.
[x(1)][x(42i)][x(4+2i)]=0
(x+1)(x4+2i)(x42i)=0
Further use arithmetic rule.
(a+b)(ab)=a2b2
Here, a=x4,b=2i
Now, the polynomial equation is,
(x+1)[(x4)2(2i)2]=0
Use arithmetic rule.
(ab)2=a22ab+b2
And i2=1
Now, the polynomial equation is,
(x+1)(x28x+16+4)=0
(x+1)(x28x+20)=0
(x3+x28x28x+20x+20)=0
x37x2+12x+20=0
Hence, the polynomial equation of giveb roots 1,42iisx37x2+12x+20=0
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2021-04-26
An elevator (mass 4850 kg) is to be designed so that themaximum acceleration is 0.0600g. What is the maximum and the minimum forces the motor should exert on the supportingcable?
I already know how to find the maximum force (just multiplyingthe maximum acceleration by the mass), but I've got no clue as tohow to find the minimum acceleration when no minimum accelerationhas been found.
asked 2021-02-09

In Figure, a stationary block explodes into two pieces and R that slide across a frictionless floor and then into regions with friction, where they stop. Piece L, with a mass of 2.6 kg, encounters a coefficient of kinetic friction μL=0.40 and slides to a stop in distance deal = 0.15 m. Piece R encounters a coefficient of kinetic friction μR=0.50 and slides to a stop in distanced R=0.30 m. What was the mass of the original block?
image

asked 2021-03-26
A pair of forces with equal magnitudes, opposite directions,and different lines of action is called a "couple". When acouple acts on a rigid object, the couple produces a torque thatdoes not depend on the location of the axis. The drawing shows acouple acting on a tire wrench, each force being perpendicular tothe wrench. Determine an expression for the torque produced by thecouple when the axis is perpendicular to the tired and passesthrough (a) point A, (b) point B, and (c) point C. Express youranswers in terms of the magnitude F of the force and the length Lof the wrench
asked 2020-11-11
The heaviest invertebrate is the giant squid, which is estimated to have a weight of about 2 tons spread out over its length of 70 feet. What is its weight in newtons.
asked 2020-11-05

(2sinα+3cosα)2+(3sinα2cosα)2=13

asked 2020-10-18

A coin with a diameter of 2.40cm is dropped on edge on to a horizontal surface. The coin starts out with an initial angular speed of 18.0 rad/s and rolls in a straight line without slipping. If the rotation slows with an angular acceleration of magnitude 1.90 rad/s, how far does the coin roll before coming to rest?

asked 2021-12-11
Factor the polynomial.
m22mm+121

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question