If a x2 + b x + c is a perfect square, then
a2 = 4 bc
b2 = 4 ac
a = 4 c
b2 = 4 a
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 )
4 x2-9 =0; solution set of the given equation is
{9/4}
{3/2}
{±3/2}
{0}
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
The second order homogenous expression in x,y
ax2+ b xy + c y2
ax2 + b x
ax+by2
ax2+by
IF x+1/x= a, then x2+ 1/x2 =
a2-2
a2+2
a2
a2+1
If 5 is a root of the equation x2- (k-1) x+10 =0; then the value of k=
-5
7
6
8
Frame an equation in x having 2 and -3 as roots.
x2+x+6=0
x2-x-6=0
x2-6=0
x2+x-6=0
2x4y2
4x8y2
2x8y2
16x8y2
Sum of the roots of the equation 4 x2 -1 = 0 is
-1/4
0
1/4
4
