Question

write the write the quadratic equation bracket (X + 5)( x-11) standard form and find the values of a,b,,c​

Answer 1

Answer:

Methods of Solving Quadratic Equations

There are three main methods for solving quadratic equations:

Factorization

Completing the square method

Quadratic Equation Formula

In addition to the three methods discussed here, we also have a graphical method. As you may have guessed, it involves plotting the given equation for various values of x. The intersection of the curves thus obtained with the real axis will give us the solutions. Let’s see the others in detail.

Factorization

The first and simplest method of solving quadratic equations is the factorization method. Certain quadratic equations can be factorised. These factors, if done correctly will give two linear equations in x. Hence, from these equations, we get the value of x. Let’s see an example and we will get to know more about it.

Example 1: Solve the equation: x2 + 3x – 4 = 0

Solution: This method is also known as splitting the middle term method. Here, a = 1, b = 3, c = -4. Let us multiply a and c = 1 * (-4) = -4. Next, the middle term is split into two terms. We do it such that the product of the new coefficients equals the product of a and c.

We have to get 3 here. Consider (+4) and (-1) as the factors, whose multiplication is -4 and sum is 3. Hence, we write x2 + 3x – 4 = 0 as x2 + 4x – x – 4 = 0. Thus, we can factorise the terms as: (x+4)(x-1) = 0. For any two quantities a and b, if a×b = 0, we must have either a = 0, b = 0 or a = b = 0.

Thus we have either (x+4) = 0 or (x-1) = 0 or both are = 0. This gives x+4 = 0 or x-1 = 0. Solving these equations for x gives: x=-4 or x=1. This method is convenient but is not applicable to every equation.

Explanation: thanks !!!