Quadratic Equations and Inequalities questions
963 published questions with worked solutions.
- The number of real values of the parameter k for which ( _ 16 x)^2 - _ 16 x + _ 16 k = 0 with real coefficients will have exactly...
- In a ABC, A and B are the roots of the equation ab(x^2+1)=c^2x, where a, b and c are the sides of the triangle. Then
- In a ABC, A and B satisfy the inequation 3x^2-4x+ 3<0. Then
- The equation x^2 + 4xy + 4y^2 - 3x - 6y - 4 = 0 represents a
- Let f(x) = ax^2 + bx + c, where a, b, c are rational, and f : Z Z , where Z is the set of integers. Then a + b is
- The largest set of real values of x for which f(x) = (x + 2)(5 - x) - 1 x^2 - 4 is a real function is
- Let f : R A = y , | , 0 y < 2 be a function such that f(x) = ^ -1 (x^2 + x + k), where k is a constant. The value of k for which...
- If f(x) is a polynomial function of the second degree such that f(-3) = 6, f(0) = 6 and f(2) = 11 then the graph of the function...
- If one of the roots of x^2 + f(a) x + a = 0 is equal to the third power of the other for all real a then
- If f(x) = 27x^3 + 1 x^3 and , are the roots of 3x + 1 x = 2 then
- Let f(x) be a polynomial function of the second degree. If f(1) = f(-1) and a_1, a_2, a_3 are in AP then f'(a_1), f'(a_2),...
- Let f(x) be a polynomial function of degree 2 and f(x)>0 for all x R . If g(x) = f(x) + f'(x) + f''(x) then for any x
- Let f(x) = x^2 + xg'(1) + g''(2) and g(x) = f(1) x^2 + xf'(x) + f''(x) then
- If x [-1, 1] then the minimum value of f(x) = x^2 + x + 1 is
- If f(x) be a quadratic polynomial such that f(0)=2, f'(0)=-3 and f''(0)=4 then _ -1 ^ 1 f(x) ,dx is equal to
- If _0^1(1+ ^4x)(ax^2+bx+c) ,dx= _0^2(1+ ^4x)(ax^2+bx+c) ,dx then the quadratic equation ax^2+bx+c=0 has
- If the point (0, ) is a point of the region bounded by the semicircle x= 9-y^ 2 and the line x=0 then the equation x^ 2 -2x- =0...
- If a, b, c are in AP and one root of the equation ax^2 + bx + c = 0 is 2 then the other root is
- In a PQR, R = 2 . If P 2 and Q 2 are the roots of the equation ax^2 + bx + c = 0 then
- If 1 ( , ) where , are roots of x^2 - a(x + 1) + 3 = 0 then
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