Find the value of k, if x – 1 is factor of p(x) = x² + x + k​

Question

Find the value of k, if x – 1 is factor of p(x) = x² + x + k​

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Amelia 1 month 2021-08-17T05:08:46+00:00 1 Answer 0 views 0

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    2021-08-17T05:10:15+00:00

    Answer:

    Hi

    x - 1 \: is \: a \: factor \\  \implies \: x - 1 = 0 \\ \therefore  \: x = 1

    p(x) = x {}^{2}  + x + k \\ p(1) = 1 {}^{2}  + 1 + k \\  \:  \:  \:  \:   \:   \:  \:  = 1 + 1 + k \\  \:  \:  \:  \:  \:  \:  = 2 + k

    p(1) \: i s \: a \: factor \\  \implies \: 2 + k = 0 \\  \therefore \: k \:  =  - 2

    Hope it helps you

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