Find the value of k, if x-1 is a factor of p(x)=kx^2-3x+k ​

Question

Find the value of k,
if x-1 is a factor of p(x)=kx^2-3x+k

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Serenity 1 week 2021-11-25T06:51:00+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-11-25T06:52:30+00:00

     \mathbb{ \ \ A\ N\ S\ W\ E\ R\:  \: }

    • p(x) = kx² – 3x + k
    • If (x – 1) is a factor of p(x)
    • x – 1 = 0
    • x = 1
    • k(1)² – 3 × 1 + k = 0
    • 2k – 3 = 0
    • 2k = 3
    • k = 3/2
    0
    2021-11-25T06:52:56+00:00

    According to the Question

    p(x) = kx² – 3x + k

    If (x – 1) is a factor of p(x)

    Therefore

    x – 1 = 0

    x = 1

    Substitute the value of x in Equation

    ⇒ k(1)² – 3 × 1 + k = 0

    ⇒ 2k – 3 = 0

    ⇒ 2k = 3

    ⇒ k = \bf\huge\frac{3}{2}


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