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Published on December 19th, 2010 In category Education | Maths

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Algebra cheat sheet- Some important formulas

Consider the quadratic equation ax2 + bx + c .  Suppose that its roots are denoted α and β.

It is possible to show that

  • the sum of the roots is α + β =  – ( b/a)
  • the product of the roots is α β is = c/a
  • For example the equation given is 3x2 -5x +c = 0 then  α + β is  3/5 and α β is  – 1

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    Consider the quadratic equation ax3 + bx2 + cx + d .  Suppose that its roots are denoted α , β and γ.

    It is possible to show that

  • the sum of the roots is α + β  + γ  =  – ( b/a)
  • the product of the roots is α β  + βγ + αγ  is = c/a
  • the product of the roots is  α βγ =  – (d/a)
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    If an equation (i.e. f(x) = 0) contains all positive co-efficients of any powers of x, it has no positive roots. Eg: x3+5x2+3x+9=0 has no positive roots as all the co-efficients of any powers of x are positive numbers

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    For a bi-quadratic equation ax4+bx3+cx2+dx+e = 0 , Suppose that its roots are denoted α , β, γ and Φ.

    It is possible to show that 

  • the sum of the roots is α + β  + γ   + Φ  =  – ( b/a)
  • Sum of the product of the roots taken three at a timeis as  , αβγ  + βγΦ + αβΦ + αγΦ  is = c /
  • Sum of the product of the roots taken two at a time = -d/a
  • the product of the roots is  α βγΦ  =  – (d/a)
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