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.
My Self Assessment
a)
Let S is the set of all real x, such that is positive, then S contains
b)
c)
d)
The equation has
a) At least one real solution
b) Exactly three real solutions
c) Has exactly one irrational solution
d) Complex roots
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
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If one root of is equal to the power of the other then show that
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If a > 0, b > 0, c > 0, prove that
Solve for x
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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.
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.
