Quadratic Equations and Inequalities questions
963 published questions with worked solutions.
- Let q be the maximum integral value of p in [0, 10] for which the roots of the equation x^2-px+ 5 4 p=0 are rational. Then the...
- If the value of real number > 0 for which x^2-5 x+1=0 and x^2- x-5=0 have a common real root is 3 2 then is equal to________.
- The equation e^ 4x +8e^ 3x +13e^ 2x -8e^x+1=0, x R has :
- Let α, β be the roots of the equation x^2 - px + r = 0 and 2 , 2β be the roots of the equation x^2 - qx + r = 0. Then the value...
- Let a, b, c, p, q be real numbers. Suppose α, β are the roots of the equation x^2 + 2px + q = 0 and , 1 are the roots of the...
- The smallest value of k, for which both the roots of the equation x^2 - 8kx + 16(k^2 - k + 1) = 0 are real, distinct and have...
- If but ^2 = 5 - 3 and ^2 = 5 - 3 then the equation having / and / as its roots is
- Difference between the corresponding roots of x^2 + ax + b = 0 and x^2 + bx + a = 0 is same and a b, then
- Product of real roots of the equation t^2x^2 + |x| + 9 = 0
- If p and q are the roots of the equation x^2 + px + q = 0, then
- If 2a + 3b + 6c = 0 (a, b, c R) then the quadratic equation ax^2 + bx + c = 0 has
- If the sum of the roots of the quadratic equation ax^2 + bx + c = 0 is equal to the sum of the squares of their reciprocals, then...
- The value of ' a ' for which one root of the quadratic equation (a^2 - 5a + 3 )x^3 + (3a - 1)x + 2 = 0 is twice as large as the...
- The number of real solutions of the equation x^2 - 3|x| + 2 = 0 is
- Let f(x) be a polynomial function of second degree. If f(1) = f(-1) and a, b, c are in A.P, then f'(a), f'(c) are in
- Let two numbers have arithmetic mean 9 and geometric mean 4. Then these numbers are the roots of the quadratic equation
- If (1 - p) is a root of quadratic equation x^2 + px + (1 - p) = 0, then its roots are
- If one root of the equation x^2 + px + 12 = 0 is 4 , while the equation x^2 + px + q = 0 has equal roots, then the value of ' q '...
- If 2a + 3b + 6c = 0, then at least one root of the equation ax^2 + bx + c = 0 lies in the interval
- The value of for which the sum of the squares of the roots of the equation x^2 - (a - 2)x - a - 1 = 0 assume the least value is
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