Quadratic Equations — Flashcards
Maharashtra Board · Class 10 · Mathematics
25 flashcards for Quadratic Equations (Maharashtra Board Class 10 Mathematics) to test yourself on key terms and facts.
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Solve: x^2 - 4x - 5 = 0 by factorisation.
Answer
Step 1: Factorise the quadratic polynomial. x^2 - 4x - 5 = (x - 5)(x + 1) Step 2: Use the zero product property. If product of two numbers is zero then at least one of them is zero. So, x - 5 = 0 o…
Solve: x^2 + 10x + 2 = 0 by completing the square.
Answer
Step 1: Write the quadratic in completed-square form. x^2 + 10x + 2 = (x + 5)^2 - 25 + 2 Step 2: Simplify. (x + 5)^2 - 23 = 0 Step 3: Rearrange. (x + 5)^2 = 23 Step 4: Take square roots. x + 5 = √…
Is x^2 + 10x + 2 = 0 a quadratic equation? Give a reason.
Answer
Yes. Step 1: Check the highest power of x. The maximum index of x is 2. Step 2: Check the coefficient of x^2. Here, a = 1, so a ≠ 0. Step 3: Match the standard form. It fits ax^2 + bx + c = 0. Answ…
Solve: x^2 + 5x - 6 = 0 and verify x = -6.
Answer
Step 1: Factorise. x^2 + 5x - 6 = (x + 6)(x - 1) Step 2: Set each factor equal to zero. x + 6 = 0 or x - 1 = 0 Step 3: Solve. x = -6 or x = 1 Step 4: Verify x = -6. (-6)^2 + 5(-6) - 6 = 36 - 30 - …
Check whether x = 2 is a solution of x^2 + 5x - 6 = 0.
Answer
Step 1: Substitute x = 2. 2^2 + 5(2) - 6 = 4 + 10 - 6 Step 2: Simplify. 4 + 10 - 6 = 8 Step 3: Compare with zero. 8 ≠ 0 Answer: x = 2 is not a solution.
Find the quadratic equation if the sum of roots is 10 and the product of roots is 9.
Answer
Step 1: Use the equation from given roots. x^2 - (sum of roots)x + product of roots = 0 Step 2: Substitute the values. x^2 - 10x + 9 = 0 Answer: The quadratic equation is x^2 - 10x + 9 = 0.
Write the quadratic equation whose roots are 2 and 5.
Answer
Step 1: Use the formula for a quadratic equation from roots. x^2 - (α + β)x + αβ = 0 Step 2: Add the roots. 2 + 5 = 7 Step 3: Find the product. 2 × 5 = 10 Step 4: Substitute. x^2 - 7x + 10 = 0 Ans…
When do you use the quadratic formula?
Answer
Use it when the equation is in the form ax^2 + bx + c = 0 and factorisation is difficult. Formula: X = (-b ± √(b^2 - 4ac)) / 2a Quick example: For x^2 + 5x - 6 = 0, a = 1, b = 5, c = -6 X = (-5 ± √(…
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