Question

obtain all other zeroes of 3x^4-6x^3-2x^2-10x-5, if two of its zeroes are √5/3 and -√5/3. plz dont spam its very useful to me bcoz my exam will be started to 25/9/2020​

Answer 1

Answer:

Roots of 3x⁴+ 6x³- 2x²- 10x - 5 = √5/3 , -√5/3 , -1 , -1

Step-by-step explanation:

Let f(x) = 3x⁴ + 6x³ - 2x² - 10x - 5

Given that, √5/3 and -√5/3 are two of the roots of f(x)

So, (x - √5/3) and (x + √5/3) are the factors of f(x)

Lets multiply (x - √5/3) with (x + √5/3)

So we get [x² - (√5/3)²] = (x² - 5/3) which is also a factor of f(x).

Lets name (x² - 5/3) as p(x).

Now, Since f(x) = p(x) • q(x) + r(x),

where q(x) is quotient and r(x) is the remainder.

$\frac{f(x)}{p(x)} = q(x) + r(x)$

Since p(x) is a factor of f(x), the remainder will be 0

So,

(3x⁴ + 6x³ - 2x² - 10x - 5)÷(x² - 5/3) = 3x²+ 6x + 3

Now, we got a quadratic equation q(x) = 3x² + 6x + 3

Taking the common terms out, we get

3x² + 6x + 3 = 3 ( x² + 2x + 1)

(x² + 2x + 1) is nothing but (x + 1)² = (x + 1)(x + 1)

So the roots are -1 and -1.

Thus, the all four roots f(x) = √5/3 , -√5/3 , -1 , -1

Brother, Please check your Question

It is 3x⁴ + 6x³ - 2x² - 10x - 5

and not 3x⁴ - 6x³ - 2x² - 10x - 5

√5/3 and -√5/3 will be roots of f(x) if it is 3x⁴ + 6x³ - 2x² - 10x - 5.

A slight change in sign has tremendous impact.

I have done this question twice in Brainly alone.

That's why I said it.

I HopeYou Find It Helpful.

Answer 2

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Step-by-step explanation:

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