8 Obtain all the zeros of the polynomial x4 +4x3
-2x2
-20x-15, if two of its zeroes are √5 and −√5
Answers
Answered by
0
Step-by-step explanation:
Since, it is given that
3
and −
3
are the zeroes of the polynomial f(x)=x
4
+4x
3
−8x
2
−12x+15, therefore, (x−
3
) and (x+
3
) are also the zeroes of the given polynomial. Now, consider the product of zeroes as follows:
(x−
3
)(x+
3
)
=(x)
2
−(
3
)
2
(∵a
2
−b
2
=(a+b)(a−b))
=x
2
−3
We now divide x
4
+4x
3
−8x
2
−12x+15 by (x
2
−3)
From the division, we observe that the quotient is x
2
+4x−5 and the remainder is 0.Now, we factorize the quotient x
2
+4x−5 as shown below:
x 2 +4x−5
=x 2
−x+5x−5
=x(x−1)+5(x−1)
=(x+5)(x−1)
Either x+5=0 or x−1=0
Hence, the remaining zeroes of f(x)=x
4 +4x 3 −8x 2 −12x+15 are −5,1.
please mark as brainliest answer
Similar questions