Question

if two zeros are square root 3 and –square root 3 then find third root of x3-4x2-3x+12

Answer 1

Answer:

x=1,12,√3,−√3

Explanation:

There appears to be error in posting the question.
As mentioned the two zeros are not √3,and√3.
I found that the two zeros must be √3,and−√3
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Given equation is 
f(x)=2x4−3x3−5x2+9x−3 ......(1)
Given that two of its zeros are x=√3,−√3
⇒(x+√3),(x−√3) are two factors of equation (1)
⇒(x+√3)(x−√3)=(x2−3) is a factor of the polynomial.

If we divide the equation (1) by the above quadratic by long division method we get another quadratic which is a factor of equation (1)
∴2x4−3x3−5x2+9x−3x2−3, we get dividend as 
2x2−3x+1

To find factors of second quadratic we use split the middle term method
2x2−2x−x+1, paring and taking out the common factors we get
2x(x−1)−(x−1)
⇒(x−1)(2x−1) 
Setting each factor =0, we obtain remaining two zeros as
x=1,12

Answer 2

This answer will help you.