Question 10 complete solution required........................................if u know more than two way to salve then suggest all way......

For example, let’s solve the equation:

x² - 5x + 6 = 0

Here, a = 1, b = -5, and c = 6. The two numbers that multiply to 6 and add to -5 are -2 and -3. Thus, we can rewrite the equation:

(x - 2)(x - 3) = 0

Setting each factor to zero gives us:

x - 2 = 0 or x - 3 = 0

So, x = 2 or x = 3.

2. Quadratic Formula

If factoring is not straightforward, the quadratic formula is a reliable alternative:

x = (-b ± √(b² - 4ac)) / (2a)

Using the same equation, x² - 5x + 6 = 0, we can apply the quadratic formula:

• a = 1, b = -5, c = 6
• Calculate the discriminant: b² - 4ac = (-5)² - 4(1)(6) = 25 - 24 = 1
• Now plug values into the formula:

x = (5 ± √1) / 2

This simplifies to:

x = (5 ± 1) / 2

Thus, we find:

• x = 3
• x = 2

3. Completing the Square

This method involves rearranging the equation into a perfect square trinomial:

• Start with the equation ax² + bx + c = 0.
• Move c to the other side: ax² + bx = -c.
• Divide by a if a ≠ 1.
• Add the square of half the coefficient of x to both sides.

For our example:

x² - 5x = -6

Take half of -5, square it: (-5/2)² = 25/4. Add this to both sides:

x² - 5x + 25/4 = -6 + 25/4

Now, simplify the right side:

-6 = -24/4, so:

x² - 5x + 25/4 = 1/4

This can be factored as:

(x - 5/2)² = 1/4

Taking the square root of both sides gives:

x - 5/2 = ±1/2

Thus, solving for x yields:

• x = 3
• x = 2

Summary of Methods

In summary, we explored three effective methods to solve a quadratic equation:

• Factoring, which is quick and intuitive when applicable.
• The quadratic formula, a universal method that works for all quadratics.
• Completing the square, which provides insight into the properties of the quadratic function.

Each method has its advantages depending on the specific equation you are dealing with. Understanding these different approaches will enhance your problem-solving skills in mathematics.