The equation has
a) At least one real solution
b) Exactly three real solutions
c) Has exactly one irrational solution
d) Complex roots
Your Answer
Let S is the set of all real x, such that is positive, then S contains
a)
b)
c)
d)
Show that square of is a rational number.
Prove if α, β are roots of the equation and γ, δ are roots of then show that
Show that for for any triangle with sides a, b, c 3 (ab + bc + ac) ≤ (a + b + c)2 < 4 (ab + bc + ca)
If one root of is equal to the power of the other then show that
Find all the real values of x which satisfy and .
If a > 0, b > 0, c > 0, prove that
Solve for x
For a ≤ 0, determine all real roots of the equation
Find the set of all x for which
Let be roots of the equations and respectively. If the system of equations and have non-trivial solutions then prove that
Solve for x in the following equation
Solve
If α, β are roots of and are roots of for some constant δ, then prove that
For every positive integer n, prove that Hence or otherwise prove that Where [ ] denotes greatest integer not exceeding x.
Let a, b, c be real numbers with a ≠ 0 and let α, β be roots of the equation . Express the roots of in terms of α, β.
If is the area of a triangle with sides a, b, c then show that . Also show that equality occurs if a = b = c
where a, b ε R then find the value of a for which equation has unequal roots for all values of b.
Let a and b the roots of the equation and those of are c and d, then find the value of a + b + c + d when a ≠ b ≠ c ≠ d.
The equation has an irrational root.
a) False
b) True
If a < b < c < d then the roots of the equation are real and distinct.
a) True
b) False
If x and y are positive real numbers and m and n are any positive integers then
Fill in the blanks
If is a root of the equation where p and q are real then (p, q) …………
. Express the roots of 
in terms of α, β.
