Exercise 1.2 || Question 1 (Parts 7 to 10) || Class 10 Math

Chapter 1
Quadratic Equations
Topic: Completing Square

Exercise.1.2, Question 1 Parts(7 to 10) Solve by completing Square

Description:

The quadratic formula is a powerful method for solving quadratic equations of the form ax^2 + bx + c = 0, where a, b, and c are constants. The formula is:

x = (-b ± √(b^2 - 4ac)) / 2a

Here's a step-by-step explanation of how to apply the quadratic formula:

1. Write down the quadratic equation in the standard form: ax^2 + bx + c = 0
2. Identify the values of a, b, and c
3. Plug these values into the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a
4. Simplify the expression inside the parentheses: b^2 - 4ac
5. Calculate the square root of this expression: √(b^2 - 4ac)
6. Add and subtract this value from -b: -b + √(b^2 - 4ac) and -b - √(b^2 - 4ac)
7. Divide both expressions by 2a: (-b ± √(b^2 - 4ac)) / 2a
8. Simplify the final expressions to get the solutions for x

The quadratic formula will always give you two solutions for the value of x. These solutions may be real or complex numbers, depending on the values of a, b, and c.

Example: Solve the quadratic equation x^2 + 5x + 6 = 0 using the quadratic formula.

Solution:

a = 1, b = 5, c = 6

x = (-(5) ± √((5)^2 - 4(1)(6))) / 2(1)
x = (-5 ± √(25 - 24)) / 2
x = (-5 ± √1) / 2
x = (-5 ± 1) / 2

So, the solutions are x = (-5 + 1) / 2 = -2 and x = (-5 - 1) / 2 = -3.

Therefore, the solutions to the quadratic equation x^2 + 5x + 6 = 0 are x = -2 and x = -3.

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