Question

Find all zeros of the polynomial P(x)=x^{3}-3x^{2}-10x+24 knowing that x = 2 is a zero of the polynomial.

Applications of integrals
ANSWERED
asked 2021-05-18

Find all zeros of the polynomial \(\displaystyle{P}{\left({x}\right)}={x}^{{{3}}}-{3}{x}^{{{2}}}-{10}{x}+{24}\) knowing that \(x = 2\) is a zero of the polynomial.

Answers (1)

2021-05-20

Step 1
The given polynomial is \(\displaystyle{P}{\left({x}\right)}={x}^{{{3}}}-{3}{x}^{{{2}}}-{10}{x}+{24}\) whose one of the factors is \(x=2\)
Divide the polynomial by \(x-2\).
Step 2
The quotient is \(\displaystyle{x}^{{{2}}}-{x}-{12}\).
Factorize the polynomial \(\displaystyle{x}^{{{2}}}-{x}-{12}\) and find the zeros
\(\displaystyle{x}^{{{2}}}-{x}-{12}={0}\)
\((x-4)(x+3)=0\)
\(x=4. x=-3\)
Hence, the zeros are \(x=4. x=-3\ and\ x=2.\)

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