Find all zeros of the polynomial 6x4+17x3-2x2+x-6 = 0
- print Print
- list Cite
Expert Answers
calendarEducator since 2010
write12,544 answers
starTop subjects are Math, Science, and Business
We can write the given polynomial 6*x^4+17*x^3-2*x^2+x-6 as:
6*x^4+17*x^3-2*x^2+x-6
=> 6x^4 + 18x^3 - x^3 - 3x^2 + x^2 + 3x - 2x - 6
=> 6x^3( x + 3) - x^2(x + 3) + x(x + 3) - 2(x + 3)
=> (x + 3)[6x^3 - x^2 + x - 2]
=> (x + 3)( 6x^3 - 4x^2 + 3x^2 - 2x + 3x - 2)
=> (x +3)(2x^2(3x - 2) + x(3x - 2) + 1(3x - 2))
=> (x +3)(3x - 2)( 2x^2 + x +1)
Equating the polynomial to 0
(x +3)(3x - 2)( 2x^2 + x +1)
x + 3 = 0
=> x1 = -3
3x - 2 = 0
=> x2 = 2/3
2x^2 + x +1 = 0
=> x3 = [-1 + sqrt (1 - 8)]/4
=> x3 = -1/4 + (i*sqrt 7) / 4
x4 = -1/4 - (i*sqrt 7) / 4
Therefore the roots or zeroes of the polynomial 6*x^4+17*x^3-2*x^2+x-6 are :
-3 , 2/3 , [(-1/4) + (i*sqrt 7)/4] , [(-1/4) - (i*sqrt 7)/4]
Related Questions
- Find all zeros of the polynomial P(x) = x^3 - 3x^2 - 10x + 24 knowing that x = 2 is a zero of the...
- 2 Educator Answers
- Find all rational zeros of P(x) = x3 - 7x + 6
- 1 Educator Answer
- What does it mean zeroes of polynomial?What does it mean zeroes of polynomial?
- 3 Educator Answers
- What's a factor of x^3 - x - 6 =0
- 1 Educator Answer
- 2cosx + 1 = 0 find x values for the interval [0, 2pi]
- 4 Educator Answers
calendarEducator since 2011
write51 answers
starTop subjects are Math and Literature
We can find the zeros of a polynomial equation by using synthetic division.
First check to see that the equation is written in descending powers of the variable.
Then look at the highest power in the equation. This will tell how many solutions (zeros) there are for the equation.
6x^4 + 17x^3 - 2x^2 + x - 6 = 0
The degree of the equation is 4; therefore, we will have 4 solutions.
Synthetic Division:
(The entire section contains 2 answers and 594 words.)
Unlock This Answer Now
Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.