Question

Find the zeros of x⁴+5x³-8x²-10x+12,if it's two zeroes are √2 and -√2

Answer 1

P(x) = x⁴ + 5x³ -8x² -10x +12

now roots = √2  and -√2  ⇒  p(x) is divisible by (x-√2)(x + √2) =  x² - 2

P(x) = (x² - 2)(x² +5x - 6)  ⇒ (x² - 2)( x² +6x - x - 6 )
                                       ⇒ (x²-2)(x+6)(x-1)

so other roots gonna be -6 and 1

hope this would b helpful...........