Question

if two.zeores of x^3-4x^2-3x+12 are+-√3 find other ​

Answer 1

Since, it is given that √3 and −√3 are the zeroes of the polynomial f(x)=x³ − 4x² − 3x +1 2, 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) = x² − 3

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.