Q3 of 108 Page 38

With the following polynomials their zeroes are given. Find their all other zeroes:


Given that 2 + √3 and 2 - √3 are the zeroes of the given polynomial.

So (x – (2 + √3)) (x – (2 - √3)) = (x – 2 - √3) (x – 2 + √3)


= x2 – 2x + √3x – 2x + 4 – 2√3 - √3x + 2√3 – 3


= x2 – 4x + 1



The other zeroes are as follows:


x2 – 2x - 35 = 0


Solving the above quadratic equation.


Sum = -2


Product = -35


So the numbers which satisfy the above condition are -7 and 5


x2 – 7x + 5x - 35 = 0


x(x – 7) + 5(x – 7) = 0


(x + 5) (x – 7) = 0


Solving the first part,


x + 5 = 0


x = -5


Solving the second part,


x – 7 = 0


x = 7


Therefore the other zeroes of the polynomials are -5 and 7.


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