In the given polynomial we have been asked to find the value of k if (3x−2) is a factor of 3x3−kx2+21x−10.
ML Aggarwal Avichal Publication, factorisation, chapter 6, question no 19
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Let us assume 3x–2=0⇒3x=2⇒x=32
Since, (3x−2) is a factor of f(x)
∴ By factor theorem,
f(32)=0
⇒3(2/3)3–k(2/3)2+21(2/3)−10=0
⇒3(8/27)−k(4/9)+14−10=0
⇒98−94k+14−10=0
⇒98−94k+4=0
⇒8−4k+36=0
⇒44−4k=0
⇒4k=44
⇒k=11