Test: equations in blogger.

The general form of a quadratic equation in x is, ax²+bx+c=0,

where a, b, c Є R & a≠0.

Results:

1.  The solution of the quadratic equation, ax²+bx+c=0 is given by

 

The expression b²-4ac =D is called the discriminant of the quadratic equation.

2.  If α and β are the roots of the quadratic equation ax²+bx+c=0, then ;

A. α+β= -

B. αβ=

C. α-β=

3.  Nature of roots:

A. Consider the quadratic equation ax²+bx+c=0 where a, b, c Є R & a≠0 then;

i.          D>0  roots are real & distinct (unequal).

ii.         D=0  roots are real & coincident (equal).

iii.       D<0  roots are imaginary.

iv.        If p+iq is one root of a quadratic equation, then the other must be the conjugate p-iq & vice versa. ( p,q Є R & i=

B. Consider the quadratic equation ax²+bx+c=0 where a, b, c Є Q & a≠0 then;

i.          If D>0 & is a perfect square, then roots are rational & unequal.

ii.         If α=p+  is one root in this case, (where p is rational &  is a surd) then the other root must be the conjugate of it i.e. β=p-  & vice versa.

4. A quadratic equation whose roots are α and β is (x-α)(x-β)=0

i.e. x²-(α+β)x+αβ =0

i.e. x²-( sum of roots)x+product of roots=0