Adv
Rajan@2021
  • 0
Guru

Find the value of the constant a and b, if (x – 2) and (x + 3) are both factors of expression x3 + ax2 + bx – 12.

  • 0

In the question there are two factors (x – 2) and (x + 3) of  expression  x+ ax+ bx – 12, and we have been asked to find the value of constant a and b. 

ML Aggarwal(avichal publication), factorisation, chapter 6, question no 22

Share

1 Answer

  1. Given,
    f(x)=x3+ax2+bx12
    Let us assume
    x2=0  and  x+3=0
    x=2  and  x=3

    Also given that, (x2) and (x+3) are factors of f(x)
      By factor theorem, f(2)=0  and  f(3)=0

    Now, f(2)=0
    23+a(2)2+b(2)12=0
    8+4a+2b12=0
    4a+2b4=0
    Dividing te equation by 2
    2a+b2=0...(i)

    And, f(3)=0
    (3)3+a(3)2+b(3)12=0
    27+9a3b12=0
    9a3b39=0
    Dividing the equation by 3
    3ab=13...(ii)

    Now, adding equation (i) and equation (ii) we get,
    (2a+b)+(3ab)=2+13
    2a+3a+bb=15
    5a=15
    a=515=3

    Substituting this value of a in equation (i)
    2a+b=2
    2(3)+b=2
    6+b=2
    b=26
    b=4

    Hence, a=3  and  b=4

    • 0
Leave an answer

Leave an answer

Browse

Choose from here the video type.

Put Video ID here: https://www.youtube.com/watch?v=sdUUx5FdySs Ex: "sdUUx5FdySs".

Captcha Click on image to update the captcha.

Related Questions