if 2by root of 3 is a zero of a polynomial root of 3x+b then b =
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Step-by-step explanation:
Since, it is given that
3
and −
3
are the zeroes of the polynomial f(x)=x
3
−4x
2
−3x+12, therefore, (x−
3
) and (x+
3
) are also the zeroes of the given polynomial. Now, consider the product of zeroes as follows:
(x−
3
)(x+
3
)
=(x)
2
−(
3
)
2
(∵a
2
−b
2
=(a+b)(a−b))
=x
2
−3
We now divide x
3
−4x
2
−3x+12 by (x
2
−3) as shown in the above image:
From the division, we observe that the quotient is x−4 and the remainder is 0.
Since x−4 is the quotient,
Hence, the third zero of f(x)=x
3
−4x
2
−3x+12 is 4.
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