Question

obtain all zeroes 3x^4+6x^3-2x^210x-5 if two of its zeroes are√5/3and√5/3

Answer 1

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

$\huge \underline {Solution:-}$

$<b >$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.

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Regards @Alan ❤️

$\huge {Be\:Brainly}$

Answer 2

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

\huge \underline {Solution:-}

Solution:−

< b ><b> 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.

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\huge {Be\:Brainly}BeBrainly