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Express the term (x+2)^(3)=x(x^(2)-1) in...

Express the term `(x+2)^(3)=x(x^(2)-1)` in the form `ax^(2)+bx+c=0(ane0)` of quadratic equation and find the coefficient of `x^(2),xandx^(0)`.

Text Solution

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Given that `(x+2)^(3)=x(x^(2)-1)`
or, `(x)^(3)+3.x^(2).2+3.x.2^(2)+2^(3)=x^(3)-x`
or, `x^(3)+6x^(2)+12x+8=x^(3)-x`
or, `x^(3)+6x^(2)+12x+8-x^(3)+x=0`
or, `6x^(2)+13x+8=0`
`:.` the required quadratic equation is `6x^(2)+13x+8=0`.
Here, coefficient of `x^(2)=6` coefficient of x=3 and coefficient of `x^(0)=8`.
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Knowledge Check

  • If (a-1)^(2)x^(2)+bx+c=0 be a quadartic equation, then

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    `ane0`
    B
    `ane1`
    C
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    1
    C
    2
    D
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