Quadratic Equations
NIOS · Class 10 · Maths
Flashcards for Quadratic Equations — NIOS Class 10 Maths. Quick Q&A cards covering key concepts, definitions, and formulas.
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Get startedWhich of these is a quadratic equation: 3x^2 = 5, x^3 + 1 = 3x^2, and x^2 + 2x + 3 = 0?
Answer
Step 1: Rewrite 3x^2 = 5 as 3x^2 - 5 = 0. This is a quadratic equation. Step 2: Rewrite x^3 + 1 = 3x^2 as x^3 - 3x^2 + 1 = 0. The highest power is 3, so it is not quadratic. Step 3: x^2 + 2x + 3 = 0 i…
Rewrite 2 + 3x + 5x^2 = 0 in standard form.
Answer
Step 1: Arrange terms in descending powers of x. Step 2: Put the x^2 term first, then x, then constant. 2 + 3x + 5x^2 = 0 5x^2 + 3x + 2 = 0 Answer: 5x^2 + 3x + 2 = 0.
Rewrite 7y^2 - 5y = 2y + 3 in standard form.
Answer
Step 1: Bring all terms to one side. 7y^2 - 5y - 2y - 3 = 0 Step 2: Combine like terms. 7y^2 - 7y - 3 = 0 Answer: 7y^2 - 7y - 3 = 0.
Solve by factorisation: (x - 4)(x + 3) = 0
Answer
Step 1: Use the zero-product idea. If (x - 4)(x + 3) = 0, then x - 4 = 0 or x + 3 = 0. Step 2: Solve each equation. x - 4 = 0 -> x = 4 x + 3 = 0 -> x = -3 Answer: x = 4 and x = -3.
Solve by factorisation: 6x^2 + 7x - 3 = 0
Answer
Step 1: Split the middle term using 6 × (-3) = -18. 6x^2 + 7x - 3 = 0 6x^2 + 9x - 2x - 3 = 0 Step 2: Group terms. 3x(2x + 3) - 1(2x + 3) = 0 Step 3: Take common factor. (2x + 3)(3x - 1) = 0 Step 4: Se…
Solve by factorisation: x^2 + 2x + 1 = 0
Answer
Step 1: Recognise the perfect square. x^2 + 2x + 1 = (x + 1)^2 Step 2: Set the square equal to zero. (x + 1)^2 = 0 Step 3: Solve. x + 1 = 0 -> x = -1 Answer: x = -1, and this is a case of two coincide…
Why does x^2 + 2x + 1 = 0 have only one distinct solution?
Answer
Step 1: Factorise the equation. x^2 + 2x + 1 = (x + 1)^2 Step 2: A squared factor becomes zero only when the inside factor is zero. x + 1 = 0 Step 3: Solve. x = -1 Concept: There is only one distinct …
Use the quadratic formula to solve 6x^2 - 19x + 15 = 0.
Answer
Step 1: Identify a, b, c. a = 6, b = -19, c = 15 Step 2: Find the discriminant. D = b^2 - 4ac = (-19)^2 - 4(6)(15) = 361 - 360 = 1 Step 3: Substitute into the formula. x = (-b ± sqrt(b^2 - 4ac)) / 2a …
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