Quadratic Equations and Inequalities questions
963 published questions with worked solutions.
- The sum of all the roots of the equation (x-1)^2 - 5|x-1| + 6 = 0, is:
- The positive integer n, for which the solutions of the equation x(x+2)+(x+2)(x+4)+....+(x+2n-2)(x+2n) = 8n 3 are two consecutive...
- Let and be the roots of equation x^2 + 2ax + (3a + 10) = 0 such that < 1 < . Then the set of all possible values of a is:
- Let , be the roots of the quadratic equation 12x^2-20x+3 =0, Z. If 1 2 | - | 3 2 , then the sum of all possible values of is :
- The smallest positive integral value of a, for which all the roots of x^4-ax^2+9=0 are real and distinct, is equal to
- If , , where < , are the roots of the equation x^2 - ( +3)x + 3 = 0 such that 1 - 1 = 1 3 , then the sum of all possible values...
- Let _ and _ be the distinct roots of 2x^2 + ( )x - 1 = 0, (0, 2 ). If m and M are the minimum and the maximum values of _ ^4+ _...
- The product of all the rational roots of the equation (x^2 - 9x + 11)^2 - (x - 4)(x - 5) = 3, is equal to :
- If α + iβ and γ + iδ are the roots of x^2 - (3-2i)x - (2i-2) = 0, i= -1 , then αγ + βδ is equal to :
- The number of solutions of the equation ( 9 x - 9 x + 2 ) ( 2 x - 7 x + 3 ) = 0 is :
- If the set of all a R, for which the equation 2x^2 + (a-5)x + 15 = 3a has no real root, is the interval ( , ), and X = x Z : < x...
- If the set of all a R - 1 , for which the roots of the equation (1 - a)x^2 + 2(a - 3)x + 9 = 0 are positive is (- , - ] [ , ),...
- Let P_n = ^n + ^n, n ∈ N. If P_ 10 = 123, P_9 = 76, P_8 = 47 and P_1 = 1, then the quadratic equation having roots 1 and 1 is :
- Let the equation x(x+2)(12-k) = 2 have equal roots. Then the distance of the point (k, k 2 ) from the line 3x + 4y + 5 = 0 is
- Let α and β be the roots of x^2+ 3x-16=0, and γ and δ be the roots of x^2+3x-1=0. If P_n = ^n+ ^n and Q_n = ^n+ ^n, then P_ 25 +...
- Consider the equation x^2 + 4x – n = 0 where n ∈ [20, 100] is a natural number. Then the number of all distinct values of n, for...
- The sum of the squares of the roots of |x-2|^2 + |x-2| - 2 = 0 and the squares of the roots of x^2 - 2|x-3| - 5 = 0, is
- For t > – 1, let _t and _t be the roots of the equation ((t+2)^ 1/7 -1 )x^2 + ((t+2)^ 1/6 -1 )x + ((t+2)^ 1/21 -1 ) = 0. If _ t...
- The number of elements in the set (a,b):2a^2+3b^2=35, a,b Z , where Z is the set of all integers, is
- Consider the two sets: A= m R: both the roots of x^2-(m+1)x+m+4=0 are real and B=[-3,5). Which of the following is not true? (JEE...
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