Q81.The number of the real roots of the equation (x + 1)2 + x −5 = 274 is ________.
What This Question Tests
The question asks for the number of real roots of a complex equation, which can be solved by analyzing the function or by considering cases after rearranging the equation.
Concepts Tested
Formulas Used
Discriminant (D = b² - 4ac)
Properties of continuous functions
📚 NCERT Sections This Tests
3.23 — The Rate Constant For The Decomposition Of Hydrocarbons Is 2.418 × 10–5S–1
Chemistry Class 11 · Chapter 3
3.23 The rate constant for the decomposition of hydrocarbons is 2.418 × 10–5s–1 at 546 K. If the energy of activation is 179.9 kJ/mol, what will be the value of pre-exponential factor.
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.
9.18 — For Fixed Distance S Between Object And Screen, The Lens Equation
Physics Class 12 · Chapter 9
9.18 For fixed distance s between object and screen, the lens equation does not give a real solution for u or v if f is greater than s/4. Therefore, fmax = 0.75 m.
📋 Question Details
- Chapter
- Quadratic Equations
- Topic
- Roots of Equations
- Year
- 2021
- Shift
- 24 Feb Shift 2
- Q Number
- Q81
- Type
- Numerical
- 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