Question

obtain all other zeros of
$3x^4 + 6x ^3 - 2x ^2 - 10x - 5$
if two of its zeroes are
$\sqrt{5 \div 3} \: and - \sqrt{5 \div 3}$

Answer 1

Hey there !!

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Since two zeroes are √(5/3) and –√(5/3), so [ x – (5/3) ] and [ x + (5/3) ] are the factors of the given polynomial.

Now, [ x – (5/3) ] [ x + (5/3) ]
= x² – (5/3)
=> 3x²–5 is a factor of the given polynomial.

Refer to the attachment for division.

3x⁴+6x³–2x²–10x–5 = (3x²–5) (x²+2x+1)
Now, x² + 2x + 1 = x² + x + x + 1
= x(x+1) + (x+1)
= (x+1) (x+1)

So, its other zeroes are –1 and –1,

Thus, all the zeroes of the given polynomial are √(5/3) , –√(5/3) , –1 and –1.

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Hope my ans.'s satisfactory.☺

Answer 2

Hello friend...!!


• The zeros of the polynomial are √ 5/3 , - √ 5/3 , -1 , -1.

Hope the attached solved picture is useful to you...!!