Question

If one zero of a polynomial x 3 – 8x 2 + 19x – 12 is 4 . Then find all the zeroes

Answer 1

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Answer 2

x = 1, 3 and 4 are the zeroes of the given polynomial.

Step-by-step explanation:

We are given the following polynomial:

$x^3 - 8x^2 + 19x - 12$

4 is a zero of given polynomial.

Thus, we can write (x-4) is a factor of the given polynomial.

$g(x) = \dfrac{x^3-8x^2+19x-12}{x-4}\\\\g(x) = x^2 - 4x + 3$

Factorizing, the obtained polynomial:

$x^2-4x+3 = 0\\x^2 -x-3x+3 = \\x(x-1)-3(x-1) = 0\\(x-3)(x-1) = 0\\x-3 = 0, x - 1 - 0\\x =3, x= 1$

Thus, x = 1, 3 and 4 are the zeroes of the given polynomial.

#LearnMore

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