Adv
MathsMentor
  • 0
Guru

Verify that 5,-2,1/3 are the zeroes of the cubic polynomial p(x)=(3x³-10x²-2x+10) and verify the relationship between its zeroes and coefficients.

  • 0

This question is taken from polynomials in which we have given a cubic equation p(x)=(3x³-10x²-2x+10) and we have to show that 5,-2,1/3 are its zeroes and we also have to verify the relationship between the zeroes and coefficient.

Kindly give me a detailed solution of this question

RS Aggarwal, Class 10, chapter 2B, question no 2

Share

1 Answer

  1. Let f(x)=31027x+10

    5,2 and 1/3 are the zeroes of the polynomial ( given )

    Therefore,
    f(5)=3(510(527(5)+10
    =3×125250135+10
    =0

    f(2)=3(210(227(2)+10
    2440+54+10
    =0

    f(1/3)=3(1/310(1/327(1/+10
    =1/810/99+10
    =0

    Verify relations :
    General form of cubic equation :a+b+cx+d
    now ,
    Consider α=5,β=2  and y=31

    α+β+y=52+1​/3=10/3=b/a

    αβ+βy+αy=5(2)+(2)(1​/3)+(5×1/3)=10+(−2)​/3+5/3=9=c/a

    and αβy=5(2)(1/3)=−10/3=d/a

    • 1
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