Q61.If one real root of the quadratic equation 81x2 + kx + 256 = 0 is cube of the other root, then a value of k is : (1) -81 (2) 100 (3) 144 (4) -300 where x and y are real numbers then y −x equals
What This Question Tests
This question tests the application of Vieta's formulas (relation between roots and coefficients) to solve for an unknown coefficient given a specific relationship between the roots of a quadratic equation.
Concepts Tested
Formulas Used
α + β = -b/a
αβ = c/a
📚 NCERT Sections This Tests
1.27 — If The Solubility Product Of Cus Is 6 × 10–16, Calculate The Maximum Molarity Of
Chemistry Class 11 · Chapter 1
1.27 If the solubility product of CuS is 6 × 10–16, calculate the maximum molarity of CuS in aqueous solution.
3.16 — The Rate Constant For A First Order Reaction Is 60 S–1. How Much Time Will
Chemistry Class 11 · Chapter 3
3.16 The rate constant for a first order reaction is 60 s–1. How much time will it take to reduce the initial concentration of the reactant to its 1/16th value?
6.11 — Dynamics Of Rotational
Physics Class 11 · Chapter 6
6.11 Dynamics of rotational the motion of extended bodies. motion about a fixed axis A large class of problems with extended bodies can be
📋 Question Details
- Chapter
- Quadratic Equations
- Topic
- Relation between roots and coefficients
- Year
- 2019
- Shift
- 11 Jan Shift 1
- Q Number
- Q61
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 5: Complex Numbers and Quadratic Equations
More from this Chapter
Q83.If the difference between the roots of the equation x2 + ax + 1 = 0 is less than √5, then the set of possible values of a is JEE Main 2007 JEE Main Previous Year Paper (1) (−3, 3) (2) (−3, ∞) (3) (3, ∞) (4) (−∞, −3)
Q72.The quadratic equations x2 −6x + a = 0 and x2 −cx + 6 = 0 have one root in common. The other roots of the first and second equations are integers in the ratio 4 : 3. Then the common root is (1) 1 (2) 4 (3) 3 (4) 2
Q61.If the roots of the equation bx2 + cx + a = 0 be imaginary, then for all real values of x, the expression 3b2x2 + 6bcx + 2c2 is (1) greater than 4ab (2) less than 4ab (3) greater than −4ab (4) less than - 4ab
Q61.The value of k for which the equation (K −2)x2 + 8x + K + 4 = 0 has both roots real, distinct and negative is (1) 6 (2) 3 (3) 4 (4) 1