Quadratic Equations and Inequalities questions
963 published questions with worked solutions.
- If x^2+9y-4x+3=0, x, y R, then x and y respectively lie in the intervals:
- The set of all values of k > –1, for which the equation (3x^2+4x+3)^2-(k+1)(3x^2+4x+2)(3x^2+4x+3)+k(3x^2+4x+2)^2=0 has real...
- If , R are such that 1-2i (here i^2=–1) is a root of z^2+ z+ =0, then ( - ) is equal to :
- Let and be the roots of x^2-6x-2=0. If a_n= ^n- ^n for n 1, then the value of a_ 10 -2a_8 3a_9 is :
- The coefficients a, b and c of the quadratic equation, ax^2+bx+c=0 are obtained by throwing a dice three times. The probability...
- The integer 'k', for which the inequality x^2-2(3k-1)x+8k^2-7>0 is valid for every x in R, is :
- The number of real solutions of the equation, x^2-|x|-12=0 is:
- The sum of all integral values of k(k 0) for which the equation 2 x-1 - 1 x-2 = 2 k in x has no real roots, is _______.
- If the sum of the squares of the reciprocals of the roots and of the equation 3x^ 2 + x - 1 = 0 is 15, then 6( ^ 3 + ^ 3 )^ 2 is...
- The equation y^2-x^2+2x-1=0 represents
- Let f(x) be a quadratic polynomial with leading coefficient 1 such that f(0) = p, p 0, and f(1) = 1/3. If the equations f(x) = 0...
- If the numbers appeared on the two throws of a fair six faced die are and , then the probability that x^ 2 + x + > 0, for all x...
- Let a, b be two non-zero real numbers. If p and r are the roots of the equation x^ 2 - 8ax + 2a = 0 and q and s are the roots of...
- Let a, b ℝ be such that the equation ax^ 2 - 2bx + 15 = 0 has a repeated root . If and are the roots of the equation x^ 2 - 2bx +...
- The minimum value of the sum of the squares of the roots of x^ 2 + (3 - a)x + 1 = 2a is
- If for some p, q, r R, not all have same sign, one of the roots of the equation (p^ 2 + q^ 2 )x^ 2 - 2q(p + r)x + q^ 2 + r^ 2 = 0...
- The sum of the cubes of all the roots of the equation x^ 4 - 3x^ 3 - 2x^ 2 + 3x + 1 = 0 is _____.
- The number of integral values of k, for which one root of the equation 2x^2-8x+k=0 lies in the interval (1, 2) and its other root...
- Let p and q be real numbers such that p 0, p^3 q and p^3 -q. If and are nonzero complex numbers satisfying + = -p and ^3 + ^3 =...
- Let α and β be the roots of x^2 - 6x - 2 = 0, with > . If a_n = ^n - ^n for n 1, then the value of a_ 10 - 2a_8 2a_9 is
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