Question

Find all the zeroes of the polynomial x4
– 5x3 + 2x2+10x-8, if two of its zeroes are 4 and 1.

Answer 1

−

2

,

2

are two zeros it means (x+

2

)(x−

2

) are its factor

or say (x

2

−2) is the factor hence we can write

x

2

−2)

x

4

−5x

3

+2x

2

+10x−8

(x

2

−5x+4

±x

4

∓2x

2

−5x

3

+4x

2

+10x∓5x

3

∓10x

4x

2

−8±4x

2

∓8

∴x

4

−5x

3

+2x

2

+10x−8=(x

2

−2)(x

2

−5x+4)

=(x

2

−2)(x−4)(x−1)

Hence other two zeros are 1,4

∴ Sum =5

Answer 2

Zero is 14 sum 5

Hope you got your answer