If a x2 + b x + c is a perfect square, then
a2 = 4 bc
b2 = 4 ac
a = 4 c
b2 = 4 a
If α and β are the roots of the equation ax2+bx+ c = 0; then the quadratic equation having 1/ α, 1/β as roots.
bx2+ax+c = 0
ax2-bx+c = 0
c x2+bx+a = 0
c x2-bx-a = 0
If (a+b) is one of the factor of a cyclic expression, then the other factors are
b+c
(b+c),(c-a)
(b-c), (c-a)
(b+c), (c+a)
Solution set of x(x-1) =0 is
{1, -1}
{-1}
{0,1}
{0,-1}
3 a2+4 b2
3 a2+4 b
3 a+4 b
3 a-4 b
Product of the roots of the equation 2 x2-3 x = 5 is
-3/2
3/2
5/2
-5/2
If 5 is a root of the equation x2- (k-1) x+10 =0; then the value of k=
-5
7
6
8
First order homogeneous expression (x,y,z as variables) is
a x + b z
a y + a z
a z + b y + c z
a ( xyz )
The second order homogenous expression in x,y
ax2+ b xy + c y2
ax2 + b x
ax+by2
ax2+by
4 x2-9 =0; solution set of the given equation is
{9/4}
{3/2}
{±3/2}
{0}
