Quadratic Equations and Inequalities questions
963 published questions with worked solutions.
- x^2 - 3|x| + 2 < 0, then x belongs to
- Let a_1, a_2, , a_n be non-negative real numbers such that a_1 + a_2 + + a_n = p and q = _ i<j a_i a_j. Then
- Let y = (x+1)(x-3) (x-2) , then all real values of x for which y takes real values, are
- Consider the following statements: 1. If x be real, then - 9 2 3x-4 x^2+1 1 2 2. If x is real, then the greatest value of...
- If a < b, then the solution x^2 + (a + b)x + ab < 0 is given by
- The solution of the inequation 4^ -x+0.5 - 7 2^ -x < 4, x R is
- Let f(x) = ax^2 + bx + c and f(-1) < 1, f(1) > -1, f(3) < -4 and a 0, then
- If for x R, 1 3 < x^2 - 2x + 4 x^2 + 2x + 4 < 3, then 9 3^ 2x - 6 3^x + 4 9 3^ 2x + 6 3^x + 4 lies between
- The range of ab if |a| 1 and a + b = 1, (a, b R), is
- If roots of the equation x^4 - 8x^3 + bx^2 + cx + 16 = 0 are positive then
- The number of complex roots of the equation x^4 - 4x - 1 = 0, is
- The product of real roots of the equation x^2 + 18x + 30 = 2 x^2 + 18x + 45 , is
- The number of irrational solutions of the equation x^2 + x^2 + 11 + x^2 - x^2 + 11 = 4, is
- The equation 4x + 9 - 11x + 1 = 7x + 4 has
- The number of solutions of 3x^2 + 6x + 7 + 5x^2 + 10x + 14 = 4 - 2x - x^2, is
- The number of solution(s) of the inequation 3x^2 + 6x + 7 + 5x^2 + 10x + 14 4 - 2x - x^2, is
- If x, y, z are three real numbers such that x + y + z = 4 and x^2 + y^2 + z^2 = 6, then the exhaustive set of values of x, is
- The number of negative integral solutions of x^2 2^ x+1 + 2^ |x-3|+2 = x^2 2^ |x-3|+4 + 2^ x-1 , is
- Let n be an odd integer such that the polynomial P_n(x) = 1 + 2x + 3x^2 + + (n+1)x^n has exactly one real root. This real root...
- If the roots of the equation 3x^2-6x+5=0 are and , then the equation whose roots are + and 2 + will be
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