Question

If two zeroes of the polynomial
$x ^{3} - 4x {}^{2} - 3x + 12$
are
$\sqrt{3}$
and
$- \sqrt{3}$
find its third zero.


want even steps please

Answer 1

Hey!!!!!

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I'll solve on paper for best understanding

The third zero is 4.

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Hope this helps

Refer to the attachment

Answer 2

Hey there ‼
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Since two given zeroes of given polynomial are 3 and –3.
x = √3 or x = – √3
( x – √3 ) ( x + √3 ) = 0
x² – 3 is a factor of given polynomial.

Refer to the attachment for division.

x³ – 4x² – 3x + 12 = ( x – 4 ) ( x – √3 ) ( x + √3 )

Thus, the zeroes of polynomial are √3, –√3 and 4.

Answer - 4 is the third zero of the given polynomial.
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Hope my ans.'s satisfactory. (^-^)