Algebra Formulas part 3

Posted By on December 21, 2014


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Algebra formulas part-2
Exponential Formulas

Quadric Equation: ax2+bx+c=0

Solutions (roots):

x1,2=b±b24ac−−−−−−−√2a

If D=b24ac is the discriminant , then the roots are

1. real and unique if D>0

2. real and equal if D=0

3. complex conjugate if D<0

Cubic Equation: x3+a1x2+a2x+a3=0

Let

QRST=3a2a219=9a1a227a32a3154=R+Q3+R2−−−−−−−√−−−−−−−−−−−−√3=RQ3+R2−−−−−−−√−−−−−−−−−−−−√3

Then solutions (roots) of the cubic equation are:

x1x2x3=S+T13a1=12(S+T)13a1+12i3(ST)=12(S+T)13a112i3(ST)

If D=Q3+R2 is the discriminant of the cubic equation, then:

1. one root is real and two complex conjugate if D>0

2. all roots are real and at last two are equal if D=0

3. all roots are real and unequal if D<0

Quartic Equation:x4+a1x3+a2x2+a3x+a4=0

Let y1 be a real root of the cubic equation

y3a2y2+(a1a34a4)y+(4a2a4a23a21a4)=0

Then solutions of the quartic equation are the 4 roots of

z2+12(a1±a214a2+4y1−−−−−−−−−−−√)z+12(y1±y214a4−−−−−−−√)=0
Algebra formulas part-2
Exponential Formulas

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Posted by Akash Kurup

Founder and C.E.O, World4Engineers Educationist and Entrepreneur by passion. Orator and blogger by hobby

Website: http://world4engineers.com