4 x2-9 =0; solution set of the given equation is
{9/4}
{3/2}
{±3/2}
{0}
Product of the roots of the equation 2 x2-3 x = 5 is
-3/2
3/2
5/2
-5/2
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)
Nature of roots of the equation 4 x2- 4 x + 1 = 0 is
Real and equal
Irrational
Complex
Real and unequal
If a x2 + b x + c is a perfect square, then
a2 = 4 bc
b2 = 4 ac
a = 4 c
b2 = 4 a
Square root of (x-2)2 . (x+1)2. (2 x+1)2 =
(x-2) (x+1) (2 x+1)
(x-2)2(x+1)2 (2 x+1)2
(x-2)4 (x+1)4(2 x+1)4
(x-2) (2 x+1)
a2+b3
a2- b3
a4+b3
a2+b6
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
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 )
3 a2+4 b2
3 a2+4 b
3 a+4 b
3 a-4 b
