Please give me detailed solution poster 10th questions with writing on how to do and how to verify the options

best regards Sainath.

To tackle a problem effectively, especially in a subject like mathematics or science, it's essential to break it down into manageable steps. Let's take a look at a typical 10th-grade question and go through the process of solving it, as well as how to verify the options. For this example, we’ll consider a math problem involving quadratic equations.

Example Problem

Consider the quadratic equation: x² - 5x + 6 = 0. We need to find the roots of this equation and verify the solutions.

Step 1: Identify the Coefficients

In a quadratic equation of the form ax² + bx + c = 0, identify the coefficients:

• a = 1
• b = -5
• c = 6

Step 2: Use the Quadratic Formula

The quadratic formula is given by:

x = (-b ± √(b² - 4ac)) / 2a

Now, substitute the values of a, b, and c into the formula:

• Calculate b² - 4ac:
  (-5)² - 4(1)(6) = 25 - 24 = 1
• Now substitute into the formula:
  x = (5 ± √1) / 2

Step 3: Solve for x

Now, calculate the two possible values for x:

• x₁ = (5 + 1) / 2 = 6 / 2 = 3
• x₂ = (5 - 1) / 2 = 4 / 2 = 2

Thus, the roots of the equation are x = 3 and x = 2.

Verification of Solutions

To ensure our solutions are correct, we can substitute them back into the original equation:

Check x = 3

Substituting x = 3 into the original equation:

(3)² - 5(3) + 6 = 0

9 - 15 + 6 = 0

0 = 0 (True)

Check x = 2

Now substituting x = 2:

(2)² - 5(2) + 6 = 0

4 - 10 + 6 = 0

0 = 0 (True)

Final Thoughts

Both values satisfy the original equation, confirming that our solutions are correct. When solving similar problems, always remember to verify your answers by substituting them back into the original equation. This not only ensures accuracy but also reinforces your understanding of the concepts involved.

Feel free to ask if you have any more questions or need further clarification on any topic!