Question

Obtain all other zeroes of 3x4 + 6x3 – 2x2 – 10x – 5, if two of its zeroes are √(5/3) and-√(5/3).​

Answer 1

Step-by-step explanation:

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

√(5/3) and-√(5/3) are zeroes of polynomial f(x).

∴ [x-√(5/3)] [x+√(5/3)] = x2-(5/3)

(See in the attachment)

Therefore, 3x2 + 6x + 3 = 3x(x + 1) +3 (x + 1)

= (3x + 3)(x + 1)

= 3(x + 1)(x + 1)

= 3(x + 1)(x + 1)

Hence, x + 1 = 0 i.e. x = – 1 , – 1 is a zero of p(x).

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

Therefore, all four zeroes of the given polynomial are:

√(5/3) and-√(5/3), −1 and −1.

Answer 2

Answer:

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