Question

HEY FRIENDS... PLEASE HELP..

Q. Find the third zero of the polynomial x^3 + 3x^2 − 2 − 6, if two of its zeroes are − √2
and √2.

Answer 1

$\Longrightarrow{\boxed{\bold{Answer: -3 }}}$

$\textbf{\underline{Step-by-step explanation :- }}$

$\textbf{\large{Error Correction :}}$ Polynomial is x³ + 3x² - 2x - 6.

So, two zeros we have are √2 and - √2.

This means we have factors ( x - √2 ) and ( x + √2 )

So their product will be?

= ( x + √2 )( x - √2 )

Identity : ( a + b )( a - b ) = a² - b²

= x² - √2²

= x² - 2

Now by doing manual division we get,

= ( Please see attachment )

[ Note : I have written x² - 0x - 2 instead of directly writing x² - 2 to do division since 0x = 0 ]

$\textbf{\underline{Hence factor is x = - 3}}$

Answer 2

The third zero will be -3