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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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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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1. 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) = x2-(5/3) = 0

(3x2−5)=0, is a factor of given polynomial f(x).

Now, when we will divide f(x) by (3x2−5) the quotient obtained will also be a factor of f(x) and the remainder will be 0.

Therefore, 3x+6x−2x−10x–5 = (3x–5)(x2+2x+1)

Now, on further factorizing (x2+2x+1) we get,

x2+2x+1 = x2+x+x+1 = 0

x(x+1)+1(x+1) = 0

(x+1)(x+1) = 0

So, its zeroes are given by: x= −1 and x = −1.

Therefore, all four zeroes of given polynomial equation are:

√(5/3),- √(5/3) , −1 and −1.