Question

If two zeroes of the polynomial x3-4x2-3x+12 are root3 and -1 find the third zero

Answer 1

Two zeros of polynomial x³ - 4x² - 3x + 12 are √3 and -√3
[Note :- you did mistake in typing . -1 can't be root of given Polynomial.]
∴ (x - √3) and (x + √3) are factors of given Polynomial
so, (x² -3) is a factor of given polynomial
Let's arrange the given polynomial ,
x³ - 4x² - 3x + 12
= x³ - 3x - 4x² + 12
= x(x² - 3) - 4(x² - 3)
= (x - 4)(x² - 3)

Hence, other factor is (x - 4) of given Polynomial
so, other zero is x = 4