Quadratic Equations and Inequalities questions
963 published questions with worked solutions.
- If triangle ABC is a right angled at A and B 2 , C 2 , are roots of the equation ax^2 + bx + c = 0, a 0, then
- Let a be an integer selected at random from the set 0, 1, 2, 3, ...9 . The probability that the equation ax^2 - ax + 1 = 0 has...
- If f(x)=2x^3+mx^2-13x+n and 2, 3 are the roots of the equation f(x)=0 then the value of 4m+5n is
- The values of b and c for which the identify f(x + 1) - f(x) = 8x + 3 is satisfied, where f(x) = bx^2 + cx + d, are
- If x is real, then the difference between the greatest and least values of x^ 2 -x+1 x^ 2 +x+1 is
- The value of k for which the equation (K - 2)x^2 + 8x + K + 4 = 0 has both roots real, distinct and negative is
- If a, b, c, d and p are distinct real numbers such that (a^2 + b^2 + c^2)p^2 - 2p(ab + bc + cd) + (b^2 + c^2 + d^2) 0, then
- If the sum of the square of the roots of the equation x^2 - ( - 2)x - (1 + ) = 0 is least, then α is equal to
- Let p, q, r ∈ R and r > p > 0. If the quadratic equation px^2 + qx + r = 0 has two complex roots α and β, then |α| + |β| is
- If a, b, c ∈ R and 1 is a root of equation ax^2 + bx + c = 0, then the curve y = 4ax^2 + 3bx + 2c, a ≠ 0 intersect x-axis at
- If α and β are roots of the equation x^2 + px + 3p 4 = 0, such that | - | = 10 , then p belongs to the set :
- The least integral value α of x such that x - 5 x^2 + 5x - 14 > 0, satisfies :
- If p and q are non-zero real numbers and ^3 + ^3 = -p, = q, then a quadratic equation whose roots are ^2 , ^2 is :
- If 1 , 1 are the roots of the equation ax^2 + bx + 1 = 0, (a 0, a, b R), then the equation x (x + b^3 ) + (a^3 - 3abx ) = 0 has...
- If α and β are roots of the equation x^2 - 4 2kx + 2e^ 4 k - 1 = 0 for some k, and ^2 + ^2 = 66, then ^3 + ^3 is equal to:
- The sum of the roots of the equation, x^2 + |2x - 3| - 4 = 0, is:
- A number x is chosen at random from the set 1, 2, 3, 4, , 100 . Define the event: A = the chosen number x satisfies (x-10)(x-50)...
- If non-zero real numbers b and c are such that f(x) > g(x), where f(x) = x^2 + 2bx + 2c^2 and g(x) = -x^2 - 2cx + b^2, (x R);...
- Let a,b,c be positive integers in arithmetic progression such that the equation ax^2+bx+c=0 has only integer solutions. Then...
- If a, b, c, d and p are distinct real numbers such that (a^2 + b^2 + c^2)p^2 - 2(ab + bc + cd)p + (b^2 + c^2 + d^2) 0 then a, b,...
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