obtain all the zeroes of the polynomial
2x4-5x3-11x2+20x+12 when 2 and -2 are two zeroes of the above polynomial.
pl.give the step..
Answers
Answer:
other two roots are 3/2 and 1.
Step-by-step explanation:
Polynomial: 2x^4 - 5x^3 -11x^2 + 20x + 12
It is given that 2 and -2 are two roots.
Hence dividing with (x - 2) and (X + 2) we get remaining easily.
Doing simple long division method.
( x - 2) ) 2x^4 - 5x^3 -11x^2 + 20x + 12 ( 2x^3 - x^2 -13x - 6
2x^4 - 4x^3 (it is (x - 2) * 2x^3 )
--------------------------------------------------
-x^3 - 11x^2
-x^3 + 2x^2 (It is (x - 2) * -x^2)
----------------------------------------------------------
-13x^2 + 20x
-13x^2 + 26x
---------------------------------------------------------------------
-6x + 12
-6x + 12
--------------------------------------------------------------------
0
Hence (2x^4 - 5x^3 -11x^2 + 20x + 12) / ( x -2) we get 2x^3 - x^2 -13x - 6
Now (X + 2) is another root, so divide 2x^3 - x^2 -13x - 6 with X + 2
Follow same division like above, we get
(2x^3 - x^2 -13x - 6) / (x + 2) = 2x^2 - 5x - 3
Now remaining is 2x^2 - 5x - 3
Root of above binomial equations are
5 + √(5*5 + 4*2*3)/2*2 and 5 - √(5*5 + 4*2*3)/2*2
i.e. 6/4 and 4/4
Hence other two roots are 3/2 and 1.
Answer:
plzz mark prashilpa as brainliest her answer is the correct answer