How can i solve the question of polynomials of exercise 2.3 . What is the best way of solving this question. This is an important question of class 10th polynomials. Obtain all other zeroes of 3×4+6×3-2×2-10x-5, if two of its zeroes are √(5/3) and – √(5/3).

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# Obtain all other zeroes of 3×4+6×3-2×2-10x-5, if two of its zeroes are √(5/3) and – √(5/3). Q.3

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Since this is a polynomial equation of degree 4, hence there will be total 4 roots.

√(5/3) and – √(5/3)are zeroes of polynomial f(x).∴(x –√(5/3)) (x+√(5/3)= x^{2}-(5/3) = 0(3xis a factor of given polynomial f(x).^{2}−5)=0,Now, when we will divide f(x) by (3x

^{2}−5) the quotient obtained will also be a factor of f(x) and the remainder will be 0.Therefore, 3x

^{4 }+6x^{3 }−2x^{2 }−10x–5 = (3x^{2 }–5)(x^{2}+2x+1)Now, on further factorizing (x

^{2}+2x+1) we get,x= x^{2}+2x+1^{2}+x+x+1 = 0x(x+1)+1(x+1) = 0

(x+1)(x+1) = 0So, its zeroes are given by:

x= −1andx = −1.Therefore, all four zeroes of given polynomial equation are:

√(5/3),- √(5/3) , −1 and −1.Hence, is the answer.