Quadratic Equations and Inequalities questions
963 published questions with worked solutions.
- Consider the quadratic equation (c - 5)x^2 - 2cx + (c - 4) = 0, c ≠ 5. Let S be the set of all integral values of c for which one...
- If α, β and γ are three consecutive terms of a non-constant G.P. such that the equations x^2 + 2 x + = 0 and x^2 + x - 1 = 0 have...
- Let and be the roots of the equation x^2-x-1=0. If p_k=( )^k+( )^k, k 1, then which one of the following statements is not true?
- Let a, b R, a 0 be such that the equation, ax^2-2bx+5=0 has a repeated root , which is also a root of the equation, x^2-2bx-10=0....
- The set of all real values of for which the quadratic equations, ( ^2+1)x^2-4 x+2=0 always have exactly one root in the interval...
- Let α and β be the roots the equation px² + qx − r = 0, where p ≠ 0. If p, q and r be the consecutive terms of a non-constant...
- Let S = sin²2θ : (sin⁴θ + cos⁴θ)x² + (sin 2θ)x + (sin⁶θ + cos⁶θ) = 0 has real roots . If α and β be the smallest and largest...
- Let the sum of the maximum and the minimum values of the function f(x) = 2x^2 - 3x + 8 2x^2 + 3x + 8 be mn where gcd(m, n) = 1....
- If 2 and 6 are the roots of the equation ax² + bx + 1 = 0, then the quadratic equation, whose roots are 1 2a + b and 1 6a + b ,...
- The coefficients a, b, c in the quadratic equation ax² + bx + c = 0 are chosen from the set 1, 2, 3, 4, 5, 6, 7, 8 . The...
- The coefficients a, b, c in the quadratic equation ax² + bx + c = 0 are from the set 1, 2, 3, 4, 5, 6 . If the probability of...
- Let x₁, x₂, x₃, x₄ be the solution of the equation 4x⁴ + 8x³ − 17x² − 12x + 9 = 0 and (4 + x₁²)(4 + x₂²)(4 + x₃²)(4 + x₄²) = 125...
- Let and be two real roots of the equation (k+1) ^2x- 2 x=(1-k), where k ( -1) and are real numbers. If ^2( + )=50, then a value...
- The least positive value of 'a' for which the equation, 2x^2+(a-10)x+ 33 2 =2a has real roots is ______________.
- Let f(x) be a quadratic polynomial such that f(–1) + f(2) = 0. If one of the roots of f(x) = 0 is 3, then its other root lies in :
- Let α, β be roots of x² + √2x − 8 = 0. If Uₙ = αⁿ + βⁿ, then U_ 10 + 2U_9 2U_8 is equal to _____.
- Consider the two sets : A= m R: both the roots of x^2-(m+1)x+m+4=0 are real and B=[-3,5). Which of the following is not true ?
- If and are the roots of the equation x^2+px+2=0 and 1 and 1 are the roots of the equation 2x^2+2qx+1=0, then ( - 1 ) ( - 1 ) ( +...
- If the range of f( ) = ^4 + 3 ^2 ^4 + ^2 , θ ∈ R is [α, β], then the sum of the infinite G.P., whose first term is 64 and the...
- Let [t] denote the greatest integer ≤ t. Then the equation in x, [x]^2+2[x+2]-7=0 has :
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