Obtain other zeroes of the polynomial
p(x) = 2x4 – x3 - 11x2 + 5x + 5
if two of its zeroes are 15 and - 15.
Answers
The correct question is,
Obtain other zeroes of the polynomial p(x) = 2x4 – x3 - 11x2 + 5x + 5
if two of its zeroes are √5 and - √5.
The other roots are 1 and -1/2
Given,
p(x) = 2x4 – x3 - 11x2 + 5x + 5
two of its zeroes are √5 and - √5.
⇒ (x-√5)(x+√5) = (x^2-√5^2) = x^2 - 5 is a zero.
When we divide the given polynomial by x^2 - 225, we get the remaining zeros.
x^2 - 5 ) 2x4 – x3 - 11x2 + 5x + 5 ( 2x^2-x-1
2x^4 - 10x^2
----------------
-x^3-x^2+5x
-x^3+5x
----------------
-x^2+5
-x^2+5
---------------
0
We have obtained, 2x^2-x-1.
2x^2-x-1 = (x-1) (2x+1)
x = 1, -1/2
Therefore, the remaining roots are 1 and -1/2
Answer:
p(x) = 2x4 – x3 - 11x2 + 5x + 5
two of its zeroes are √5 and - √5.
⇒ (x-√5)(x+√5) = (x^2-√5^2) = x^2 - 5 is a zero.
When we divide the given polynomial by x^2 - 225, we get the remaining zeros.
x^2 - 5 ) 2x4 – x3 - 11x2 + 5x + 5 ( 2x^2-x-1
2x^4 - 10x^2
----------------
-x^3-x^2+5x
-x^3+5x
----------------
-x^2+5
-x^2+5
---------------
0
We have obtained, 2x^2-x-1.
2x^2-x-1 = (x-1) (2x+1)
x = 1, -1/2
Therefore, the remaining roots are 1 and -1/2