Question

if 2 and -2 are the zeros of the polynomial x4+x3-34x2-4x+120 find all the zeros of Given polynomial ​

Answer 1

Answer:

u can do it by division algorithm.ti know all zeros it will help u

Answer 2

Step-by-step explanation:

It is given that 2 and −2 are zeroes of the polynomial 

${x}^{4} + {x}^{3} - 34 {x}^{2} - 4x + 120$

that is (x+2)(x-2)=

${x}^{2} - 4$

Therefore, we divide the polynomial 

${x}^{4} + {x}^{3} - 34 {x}^{2} - 4x + 120$

as shown in the above image:

From the above division, we conclude that the quotient is

${x}^{2} + x - 30$

and the remainder is 0.

Now, let us factorize the quotient 

${x}^{2} + x - 30$

to find the other zereos of the given polynomial:

${x}^{2} + x - 30 = 0\\ {x}^{2} + 6x - 5x - 30 = 0 \\ x(x + 6) - 5(x + 6) = 0 \\ (x - 5)(x + 6) = 0 \\ \\ if \: x - 5 = 0 \\ then \\ x = 5 \\ if \: x + 6 = 0 \\ then \: x = - 6$

so all the zeroes are 2 , -2,5,-6

thanks for asking

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by rakhithakur