Find all zeros of f(x)=x^3-4x^2+x+6

Braxton Pugh

Braxton Pugh

Answered question

2021-09-07

Find all zeros of f(x)=x34x2+x+6

Answer & Explanation

jlo2niT

jlo2niT

Skilled2021-09-08Added 96 answers

Consider the function f(x)=x34x2+x+6
Find all the zeros.
Zeroes of the polynomials f(x) are the values of x where f(x)=0
Find the first zero by Hit an Trial method.
f(1)=(1)34(1)x21+6=0
Implies (x+1) is a factor of f(x)
Hence, f(x)=(x+1)g(x)
Factorize f(x)
x34x2+x+6=x3+(x25x2)+(5x+6x)+6
=x2(x+1)5x(x+1)+6(x+1)
=(x+1)(x25x+6)
=(x+1)(x3)(x2)
Therefore,
f(x)=(x+1)(x3)(x2)
Hence f(x)=0 at x=,1,3,2.
Zeroes of f(x) are 1,3 and 2

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