In this question we have been asked to find the value of a from given polynomial 6×3 + 5×2 + ax -2, if 2x +1 is one factor of given polynomial
ML Aggarwal Avichal Publication factorisation, chapter 6, question no 18
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Let us assume
2x+1=0
⇒2x=−1
⇒x=−1/2
Since, (2x+1) is a factor of f(x) [Given]
∴ By factor theorem,
f(−1/2)=0
⇒6(−1/2)3+5(−1/2)2+a(−1/2)−2=0
⇒6(−1/8)+5(1/4)−(−1/2)−2=0
⇒−3/4+5/4−2a−2=0
⇒−3+4−2a−8=0
⇒−6−2a=0
⇒2a=−6
⇒a=−3
Therefore a= -3