For what value of θ, 1 lies between the roots of the quadratic equation 3x^2 – 3sinθ x – 2cos^2θ = 0?(a) 2nπ + π/6 < θ < 2nπ + 5π/6(b) 2nπ + π/3 < θ < 2nπ + 5π/3(c) 2nπ + π/6 ≤ θ ≤ 2nπ + 5π/6(d) 2nπ + π/3 ≤ θ ≤ 2nπ + 5π/3This question was posed to me during an interview.This interesting question is from Applications of Quadratic Equations topic in division Complex Numbers and Quadratic Equations of Mathematics – Class 11

For what value of θ, 1 lies between the roots of the quadratic equati

1.	For what value of θ, 1 lies between the roots of the quadratic equation 3x^2 – 3sinθ x – 2cos^2θ = 0?(a) 2nπ + π/6 < θ < 2nπ + 5π/6(b) 2nπ + π/3 < θ < 2nπ + 5π/3(c) 2nπ + π/6 ≤ θ ≤ 2nπ + 5π/6(d) 2nπ + π/3 ≤ θ ≤ 2nπ + 5π/3This question was posed to me during an interview.This interesting question is from Applications of Quadratic Equations topic in division Complex Numbers and Quadratic Equations of Mathematics – Class 11
Answer» RIGHT choice is (a) 2nπ + π/6 < θ < 2nπ + 5π/6 The best explanation: Let, f(x) = 3x^2 – 3sinθ x – 2cos^2θ The coefficient of x^2 > 0 f(1) < 0 So, 3 – 3sinθ – 2cos^2θ < 0 => 2sin^2θ – 3sinθ + 1 < 0 => (2sinθ – 1)(sinθ – 1) < 0 => ½2nπ + π/6 < θ < 2nπ + 5π/6

Discussion

No Comment Found

Related InterviewSolutions

What will be the product of b * c if the equations x^2 + bx + c = 0 and x^2 + 3x + 3 = 0 have one common root?(a) 3(b) 4(c) 6(d) 9I had been asked this question in quiz.Question is from Quadratic Equations in division Complex Numbers and Quadratic Equations of Mathematics – Class 11
If, α and β are the roots of the equation 2x^2 – 3x – 6 = 0, then what is the equation whose roots are α^2 + 2 and β^2 + 2?(a) 4x^2 + 49x + 118 =0(b) 4x^2 – 49x + 118 =0(c) 4x^2 – 49x – 118 =0(d) x^2 – 49x + 118 =0The question was posed to me in a national level competition.My doubt is from Quadratic Equations in division Complex Numbers and Quadratic Equations of Mathematics – Class 11
A real number ‘a’ is called a good number if the inequality (2x^2 – 2x – 3) / (x^2 + x + 1) ≤ a is satisfied for all real x. What is the set of all real numbers?(a) (-∞, 10/3](b) (10/3, ∞)(c) [10/3, ∞)(d) [-10/3, ∞)This question was posed to me during a job interview.Question is from Applications of Quadratic Equations in division Complex Numbers and Quadratic Equations of Mathematics – Class 11
What is the number of solution(s) of the equation |√x – 2| + √x(√x – 4) + 2 = 0?(a) 2(b) 4(c) No solution(d) Infinitely many solutionsThis question was posed to me during an internship interview.This intriguing question originated from Applications of Quadratic Equations topic in division Complex Numbers and Quadratic Equations of Mathematics – Class 11
What will be the sum of b + c if the equations x^2 + bx + c = 0 and x^2 + 3x + 3 = 0 have one common root?(a) 2(b) 4(c) 6(d) 8I got this question in examination.Origin of the question is Quadratic Equations topic in division Complex Numbers and Quadratic Equations of Mathematics – Class 11
If, (a + 1)x^2 + 2(a+1)x + (a – 2) = 0, then, for what parameter of ‘a’ the given equation have equal roots?(a) (-∞, -1)(b) [-1, ∞)(c) (0, 1)(d) Not possibleI got this question in an international level competition.This key question is from Applications of Quadratic Equations in portion Complex Numbers and Quadratic Equations of Mathematics – Class 11
If p and q are the roots of the equation x^2 + px + q =0 then, what are the values of p and q?(a) p = 1, q = -2(b) p = 0, q = 1(c) p = -2, q = 0(d) p = -2, q = 1The question was asked in quiz.The query is from Quadratic Equations topic in section Complex Numbers and Quadratic Equations of Mathematics – Class 11
Which one is the complete set of values of x satisfying log x2 (x + 1) > 0?(a) (1, ∞)(b) (-1, 0) – {0}(c) (-1, 1) – {0}(d) (1, 0) ∪ (1, ∞)The question was asked during an interview.My question is from Applications of Quadratic Equations in section Complex Numbers and Quadratic Equations of Mathematics – Class 11
If, x^4 + 4x^3 + 6ax^2 + 6bx + c is divisible by x^3 + 3x^2 + 9x + 3. Then, what is the value of a + b + c?(a) 4(b) 6(c) 7(d) 10The question was asked in a job interview.I want to ask this question from Applications of Quadratic Equations in portion Complex Numbers and Quadratic Equations of Mathematics – Class 11
What will be the value of f(x) if, 2A, A + B, C are integers and f(x) = Ax^2 + Bx + C = 0?(a) Natural Number(b) Unpredictable(c) Integer(d) Complex NumberThe question was asked in semester exam.This intriguing question comes from Applications of Quadratic Equations topic in chapter Complex Numbers and Quadratic Equations of Mathematics – Class 11

Discussion

No Comment Found

Related InterviewSolutions

Reply to Comment