Q. 3 A4.9( 11 Votes )

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

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

So (x - √2) (x + √2) = x2 - 2

The above relation is same as (a + b) (a – b) = a2 – b2

Here a = x and b = √2

The other zeroes are as follows:

2x2 – 3x + 1 = 0

Solving the above quadratic equation.

Sum = -3

Product = 2

So the numbers which satisfy the above condition are -2 and -1

2x2 – 2x - x + 1 = 0

2x(x – 1) – 1(x – 1) = 0

(2x – 1) (x – 1) = 0

Solving the first part,

2x-1 = 0

2x = 1

x = 1/2

Solving the second part,

x – 1 = 0

x = 1

Therefore the other zeroes of the polynomials are 1/2 and 1.

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