Question

find all zeros of the polynomial 2x⁴-9x³+5x²+3x-1 if twovof its zeros are 2+root3 and 2-root3.

Answer 1

Hii friend,

P(x) = 2X⁴ - 9X³ + 5X² + 3X -1

Let,

Alpha = 2+✓3 and Beta = 2-✓3

Alpha + Beta = 2+✓3 + 2-✓3 = 4

Alpha × Beta = (2+✓3)(2-✓3) = (2)² - (✓3)² = 4-3 = 1.

THEREFORE,

Required polynomial = X²-(Alpha+ Beta)X + Alpha × Beta.

= X²-4X+1 is the factor of polynomial 2X⁴-9X³+5X+3X-1.

DIVIDE THE POLYNOMIAL 2X⁴-9X³+5X2+3X-1 BY X²-4X+1

AND AFTER DIVING THE POLYNOMIAL... FACTORIES THE QUOTIENT... YOU WILL GET THE ALL ZEROS OF THE POLYNOMIAL...

HOPE U WILL UNDERSTAND THIS.. :-)

Answer 2

hope this will help u.....