Question

obtain all the zeroes of 3x^4+6x^3-2x^2-10x-5 if two of its zeroes are root5/3 and -root5/4​

Answer 1

Step-by-step explanation:

Let p(x) = 3x4 + 6x3 – 2x2 – 10x - 5

Since x =√(5/3) is a zero , x – √(5/3) is a factor

& x = –√(5/3) is a zero , x + √(5/3) is a factor

Hence ("x +" √(5/3)) ("x –" √(5/3)) is also a factor

= (x2 – (√(5/3))^2) = (x2 – 5/3)

Now by dividing the given polynomial by (x2 – 5/3)

We can find out other factors

Now, we factorize 3x2 + 6x + 3

We find roots using splitting the middle term method

= 3x2 + 3x + 3x + 3

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

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

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

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

= 3(x + 1)2

Hence, x + 1 = 0

i.e. x = – 1 , – 1 is a zero of p(x)

Therefore, the zeroes of p(x) are√(5/3), -√(5/3), −1 and – 1.

Answer 2

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