Question

If √2 is one zero of the polynomial (2x^4-3x^3-3x^2+6x-2) , find all the zeroes of the given polynomial

Answer 1

Given √2 is one of the root of f(x) = 2x⁴ -3x³ -3x² +6x -2

We know irrational roots always occur in pair , so other root will be -√2

Therefore we've two factors of f(x) → (x-√2)(x+√2) = x² - 2

On dividing f(x) by (x²-2) , we get ,

f(x) = (x²-2)(2x²-3x-1) = (x²-2)(2x² -2x -x -1) = (x²-2)(2x-1)(x-1) = 0

Hence other roots are x = 1/2 and x = 1

All roots x = √2 , -√2 , 1/2 , 1

Hope this assists.