Question

Find all zeroes of the polynomial (2x- 9x3+ 5x2 + 3x-1) if two of its zeroes are
(2+√3) and (2-√3).

Answer 1

Hey brainliac...

Here's your answer...

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HOPE IT WORKS..

@Rêyaañ11

Answer 2

Hii friend,

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,

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

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

THEREFORE,

G(x) = X²-4X+1

Divide the polynomial 2X⁴ - 9X³ + 5X² + 3X-1 by X² - 4X+1.

We get,

Remainder = 0 and Quotient = 2X²-X-1

Factories the Quotient 2X² - X -1 . Then we will get the two zeros of the polynomial 2X⁴ - 9X³ + 5X² + 3X -1

2X² - X - 1

= 2X² - 2X + X -1

= 2X(X-1) + 1( X-1)

= (X-1) or ( 2X+1)

X-1 = 0. or 2X+1 = 0

X = 1. or 2X = -1

X = 1. or X = -1/2.


THEREFORE,

ALL ZEROS OF THE QUADRATIC POLYNOMIAL 2X⁴ - 9X³ + 5X² + 3X -1 ARE 2+✓3 , 2-✓3 , 1 , -1/2.


HOPE IT WILL HELP YOU...... :-)