Quadratic Equations and Inequalities questions
963 published questions with worked solutions.
- If , be unequal real roots of the equation ax^2 + bx + c = 0 where a, b, c are real and is the solution of 2ax + b = 0 then
- If , are the roots of x^2 + px + q = 0 and , are the roots of x^2 + px - r = 0 then - - - - is equal to
- If x^3 - mx^2 - 3x + 2 = 0 has two roots equal in magnitude but opposite in sign then m is
- If the equations 4x^2 - x - 1 = 0 and 3x^2 + ( + )x + - = 0 have a common root then the rational values of and are
- If ax^2 + bx + 1 = 0, a R, b R, does not have distinct real roots then the least value of 3a - 2b is
- Let f(x) = ax^2 - bx + c^2, b 0 and f(x) 0 for all x R. Then
- If f(x)=x^2+2bx+2c^2 and g(x)=-x^2-2cx+b^2 such that f(x)> g(x) then the relation between b and c is
- 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 ac,...
- The value of p for which one root of the quadratic equation (p^2-5p+3)x^2+(3p-1)x+2=0 is twice as large as the other, is
- If the equation x^2-2x+3=0 has positive roots for some real then
- , are the roots of x^2 - px + q = 0 and , , are the roots of x^3 - ax^2 + bx - c = 0. Then
- Let P, A, B, C be four collinear points in order, the distances of A, B, C from P being a, b, c respectively. If the equation...
- If x^2 + px + q is an integer for all integral values of x then
- If 4x^2 + 4x + 12 ^2 47 for all x R then can have the value
- Let f(x) = 5a^2 + 4(x-1) - x^2, x R and a is a real constant. If the maximum value of f(x) is 20 then a is
- If px^2 + qx + r = 0 has no real roots for real values of p, q, r and 4p + 2q + r > 0 then
- Let , be roots of the equation ax^2+bx+c=0 and =b^2-4ac. If + , ^2+ ^2, ^3+ ^3 are in GP then
- The number of values of a for which (x^2+x+1)a^2-(x^2+2)a-3(2x^2+3x+1)=0 will be an identity in x is
- If , are two values of satisfying the equation ^2 +p +q=1 then
- The set of values of a for which the graph of the function f(x)=a(x^2+1)+x is always above the x-axis is
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