Question

Factorise: 2x⁴ + 3x³ + x² + x + 4

Answer 1

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

To find : All the zeroes of this polynomial, 2x⁴ -3x³ - 3x² + 6x - 2

Solution : It is given that √2 and -√2 are the zeroes of this polynomial, 2x⁴ -3x³ - 3x² + 6x - 2

Therefore, (x+√2)(x-√2) i.e x² - 2 is the factor of this polynomial, 2x⁴ -3x³ - 3x² + 6x - 2.

Now, let us divide the given polynomial by x²-2

For other zeroes,

2x² - 3x + 1 = 0

By splitting middle term,

=> 2x² - 2x - x + 1 = 0

=> 2x ( x - 1 ) - 1 ( x - 1 ) = 0

=> (2x-1)(x-1) = 0

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

=> x = 1/2 and 1

Therefore, all the zeroes of this polynomial, 2x⁴ -3x³ - 3x² + 6x - 2 are 1, 1/2, √2 and -√2.

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