Paste your question to our Mathbee AI Mentor below to get an instant step-by-step solution.
Quadratic Equations
NCERT Exemplar
CBSE
Grade 10
Question:
Which of the following is a quadratic equation? (a) $x^2 + 2x + 1 = (4 - x)^2 + 3$ (b) $-2x^2 = (5 - x)\left(2x - \dfrac{2}{5}\right)$ (c) $(k + 1)x^2 + \dfrac{3}{2}x = 7$, where $k = -1$ (d) $x^3 - x^2 = (x - 1)^3$
Step-by-Step Solution
Key Concept: Expand all terms and check if the resulting degree is exactly 2.
Expand option 4: $x^3 - x^2 = x^3 - 3x^2 + 3x - 1 \Rightarrow 2x^2 - 3x + 1 = 0$. [0.5 Mark] This is of the form $ax^2 + bx + c = 0$ with $a = 2 eq 0$, so it is a quadratic equation. [0.5 Mark]
--- 🎯 Official CBSE Marking Scheme: Expanding cubic terms and cancelling $x^3$: 0.5 Mark Identifying degree 2 equation: 0.5 Mark
Correct Answer:$x^3 - x^2 = (x - 1)^3$
Mathbee AI Mentor (Free Demo)
Confused by the solution? Ask the AI to explain a specific step, tell you where you went wrong, or break down the key trap in this question.
Master Quadratic Equations with Mathbee
Practice this topic under real exam conditions with strict timers, or ask our AI Mentor to explain the concepts step-by-step.