Question

Find all zeroes of 3x⁴+6x³-2x²-10x-5 ,if two of its zeros are√(5/3 )and -√(5/3)

Answer 1

Ans:- Given:-

p(x) = 3x⁴+6x³-2x²-10x-5

Zeroes = √5/√3 and -√5/√3

To find other zeroes

Solution:-

if √5/√3 and -√5/√3 are the zeroes then,

(x + √5/√3)(x -√5/√3)

= x² - 5/3

= 3x² - 5

Now, divide the polynomials 3x⁴+6x³-2x²-10x-5 by 3x² - 5

=> (3x⁴+6x³-2x²-10x-5) ÷ (3x² - 5)

=> (3x⁴+3x³+3x³+3x²-5x²-5x-5x-5) ÷ (3x² - 5)

=> (3x³(x+1)+3x²(x+1)-5x(x+1)-5(x+1)) ÷ (3x²-5)

=> (x+1)(3x³+3x²-5x-5) ÷ (3x²-5)

=> (x+1)(3x²(x+1)-5(x+1)) ÷ (3x²-5)

=> (x+1)(x+1)(3x²-5) ÷ (3x²-5)

=> (x+1)(x+1)

now,

=> x+1=0

=> x= (-1)

=> x+1 = 0

=> x = (-1)

hence -1 and -1 are the other zeroes of the polynomials

here is your answer

hope it will help you