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Find all the zeroes of 2x4 - 3x3 - 3x2 + 6x - 2, if you know that two of its zeroes are √2 and - √2

Solution:

The zeroes of a polynomial are the values of x which satisfies the equation.

Given √2 and - √2 are the zeroes of the polynomial 2x4 - 3x3 - 3x2 + 6x - 2. 

⇒ x - √2 and x + √2 are the zeroes of the polynomial.

Using the algebraic identity a2 - b2  = (a - b)(a + b)

⇒ (x - √2) (x + √2) = x2 - (√2)2 

⇒ x2 - 2 is a factor of the polynomial 2x4 - 3x3 - 3x2 + 6x - 2.

We will use the long division method to divide the polynomials

Find all the zeroes of 2x4 - 3x3 - 3x2 + 6x - 2, if you know that two of its zeroes are √2 and - √2

2x4 - 3x3 - 3x2 + 6x - 2 = (x2 - 2 )(2x2 - 3x + 1)

We will split the middle term of the polynomial 2x2 - 3x + 1 to find the factors of the polynomial.

⇒ 2x2 - 2x - 1x + 1

⇒ 2x( x - 1) - 1( x - 1)

⇒ (2x - 1)( x - 1)

Put both the factors equal to zero.

2x - 1 = 0 and x - 1 = 0

x = ½ and x = 1

Thus, the zeroes of the polynomial 2x4 - 3x3 - 3x2 + 6x - 2 are ½ , 1, √2 and - √2

☛ Check: NCERT Solutions for Class 10 Maths Chapter 2

Find all the zeroes of 2x4 - 3x3 - 3x2 + 6x - 2, if you know that two of its zeroes are √2 and - √2

Summary:

The zeroes of the polynomial 2x4 - 3x3 - 3x2 + 6x - 2 are ½ and 1 when we know that two of its zeroes are √2 and - √2

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