Quadratic Equations and Inequalities questions
963 published questions with worked solutions.
- In each question, match every entry of Column I with the correct entry of Column II. (An entry of Column II may be used more than...
- In each question, match every entry of Column I with the correct entry of Column II. (An entry of Column II may be used more than...
- In each question, match every entry of Column I with the correct entry of Column II. (An entry of Column II may be used more than...
- Let a, b, c be real such that ax^2 + bx + c = 0 and x^2 + x + 1 = 0 have a common root. STATEMENT-1: a = b = c. STATEMENT-2: Two...
- The graph of the curve x^2 + y^2 - 2xy - 8x - 8y + 32 = 0 falls wholly in
- If f(x) = (x^2 - x + 2)(x^2 - 4) then the set x f(x) > 0, x R is equal to
- The equation ^4 + ^2 + = 0 admits of real solutions for if
- ax^2 + bx + c = 0 is an equation whose sum of roots exceeds 2 but the product of roots is less than 2. Then
- If , be the positive roots of a quadratic equation such that | - | = 1 and + = 52 then the quadratic equation is
- For all x R, x^2 + 2ax + 10 - 3a > 0. The interval in which a lies is
- The number of positive integral solutions of (x, y) when x^2 - 4xy + 6y^2 - 2x - 20y = 29 is
- For the equation 3x^2 + px + 3 = 0 (p > 0), if one of the roots is square of the other then p is equal to
- If b > a then the equation (x - a)(x - b) = 1 has
- If the roots of the equation x^2 - 10cx - 11d = 0 are a, b and those of x^2 - 10ax - 11b = 0 are c, d then the positive value of...
- Let f(x) = (1+b^2)x^2 + 2bx + 1 and m(b) the minimum value of f(x) for a given b. As b varies, the range of m(b) is
- Let a, b, c be the lengths of sides of a scalene triangle. If the roots of the equation x^2 + 2(a+b+c)x + 3 (ab + bc + ca) = 0 (...
- Let f(x) = x^2 - 6x + 5 x^2 - 5x + 6 . Match the expression/statements in **Column I** with expression/statements in **Column...
- Let a, b, c, p, q be real numbers. Suppose , are the roots of the equation x^2 + 2px + q = 0 and , 1 are the roots of the...
- Let and be the roots of x^2 - 6x - 2 = 0, > . If a_n = ^n - ^n, n 1 then the value of a_ 10 - 2a_8 2a_9 is equal to
- Let α and β be the roots of equation x^2 - 6x - 2 = 0. If a_n = ^n - ^n, n 1, then the value of a_ 10 - 2a_8 2a_9 is equal to
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