Adv
Rajan@2021
  • 0
Guru

If (x-2) is a factor of the expression 2×3 +ax2 +bx -14 and when the expression is divided by (x-3), it leaves a remainder 52, find the values a and b.

  • 0

If (x-2) is a factor of the expression 2xcube+axsquare+bx-14 and when the expression is divided by (x-3), it leaves a remainder 52, find the values a and b.

ML Aggarwal Avichal Publication Factorisation, chapter 6, question no 25

Share

1 Answer

  1. Let (x−2) is a factor of the given expression.
    Given expression, 2x3+ax2+bx−14=0
    2(2)3+a(2)2+b(2)−14=0
    16+4a+2b−14=0
    4a+2b+2=0
    4a+2b=−2
    2a+b=−1       …..(i)
    and when given expression is divided by (x−3)
    ∴2x3+ax2+bx−14∣x=3​=52
    2(3)3+a(3)2+b(3)−66=0
    54+9a+3b−66=0
    9a+3b=12
    3a+b=4         ……(ii)
    Solving equation (i) and (ii),
    2a+b=−1
    3a+b=4
    (−) (−)   (+)
    _____________________
    −a=−5                          ⇒a=5
    from (ii), 3×5+b=4
    b=4−15=−11
    ∴a=5 and b=−11

    • 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