Question

IF YOU ANSWER I WILL MARK IT THE BEST...If -1 and 2 are two zeroes of the polynomial 2x3- x2 - 5x -2, find its third zero.​

Answer 1

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Answer 2

Since, it is given that 3 and −3 are the zeroes of the polynomial f(x)=x3−4x2−3x+12, 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(∵a2−b2=(a+b)(a−b))=x2−3

We now divide x3−4x2−3x+12 by (x2−3) as shown in the above image:

From the division, we observe that the quotient is x−4 and the remainder is 0.

Since x−4 is the quotient,

Hence, the third zero of f(x)=x3−4x2−3x+12 is 4.

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