Question: What are the possible solutions for the quadratic equation “2x² – 3x – 5 = 0”?
- x = 1 and x = -5
- x = 2 and x = -3
- x = √5 and x = -√5
- x = 5/2 and x = -1
Answer: D) x = 5/2 and x = -1.
2x² – 3x – 5 = 0 Solution:
- Factoring: Try factoring the equation into two expressions that multiply. It turns out that you can rewrite the equation as (2x + 1)(x – 5) = 0. Therefore, either 2x + 1 = 0 or x – 5 = 0. Solving for x in each case gives you x = -1/2 and x = 5, respectively. However, in quadratic equations, negative multiples of solutions are also valid, so x = 5/2 and x = -1 are the final solutions.
- Quadratic Formula: Another method is using the quadratic formula, which is a general formula for solving any quadratic equation. The formula is x = (-b ± √(b^2 – 4ac)) / 2a, where a, b, and c are the coefficients of the quadratic equation (in this case, a = 2, b = -3, and c = -5). Plugging these values into the formula, we get x = (3 ± √(9 + 40)) / 4 = (3 ± √49) / 4 = (3 ± 7) / 4, which leads to x = 5/2 and x = -1.
1 Crore in Lakhs
When it comes to understanding large sums of money, converting between different units is essential. For instance, 1 crore is equivalent to 100 lakhs. This means that if you have 1 crore in your bank account, you can confidently say you possess 100 lakhs. This conversion is particularly useful in financial discussions, investments, and real estate transactions in India. Knowing how to translate crores into lakhs can help you make informed decisions about your finances, enabling you to budget and allocate resources effectively. So, the next time you hear someone mention a crore, remember it equals 100 lakhs!
