Question

29. Find other zeroes of the polynomial: x - 7x2 + 12 if it is given that two of its zeroes are v3 and -
-V3​

Answer 1

Answer:

It is given that 2+ 3​ ,2− 3​  are two zeroes of the polynomial f(x)=2x 4 −9x 3 +5x 2 +3x−1∴(x−(2+ 3​ ))(x−(2− 3​ ))=(x−2− 3​ )(x−2+ 3​ )                                                            =(x−2) 2 −( 3​ ) 2                                                        

   =x 2 −4x+4−3                                                          

 =x 2 −4x+1∴(x−(2+ 3​ ))(x−(2− 3​ ))=x 2 −4x+1 is a factor of f(x)

∴f(x)=(x 2 −4x+1)(2x 2 −x−1)Hence, the other two zeroes of f(x) are the zeroes of the polynomial 2x 2 −x−12x 2 −x−1=(2x+1)(x−1)Hence, the other two zeroes are − 21​ ,1.