Theory of Equat...

What is the number of real roots of the equation A²/x + B²/(x – 1) = 1, where A and B are real numbers not equal to zero?

If the equations x² – kx – 21 = 0 and x² – 3kx + 35 = 0 have a common root, the value of k is

The number of real roots of = 9 is

If one root of the equation x² + mx + 12 = 0 is 4 and the equation x² + mx + n = 0 has equal roots, then the value of n is

If the roots of the equation ax² + bx + c = 0 are such that their sum is equal to the sum of their squares, then

If the roots of the equation x² + a² = 8x + 6a are imaginary, then

The values of x, which satisfy both the equations x² -1 ≤ 0 and x² -x - 2 ≥ 0 lie in

If and are the roots of the equation x² + x + 1 = 0, then the equation with roots ¹⁹ and ⁷ is

The number of real solution of |x |² + 3| x | + 2 = 0 is

^{_{If and are the roots of the equation ax}2 _{+ bx + c = 0, then the equation whose roots are is}}

If a > 0, the roots of a(x² + 1) = x(a² + 1) are

If the product of the roots of the equation mx² + 6x + (2m - 1) = 0 is -1, then the value of m is

If one root of the equation x² + px + q = 0 is double the other, then is

If the sum of the roots of the equation (m + 1)x² + 2mx + 3 = 0 is 1, then the value of m is

The equation x - = 1 - has

The number of real roots of the equation (x – 1)² + (x – 2)² + (x – 3)² = 0 is

If and are the roots of the equation px² + qx + r = 0, then what is the value of ³ + ³?

If one root of the equation ax² + bx + c = 0 is double the other, then

If , and are the roots of x³ - 2x² + x - 1 = 0, then the value of 1/ + 1/ + 1/ is

For what value of m will the equation

(m + 1) x² + 2 (m + 3) x + m + 8 = 0 have equal roots?