Question

write the name of the methods for solving a quadratic equation​

Answer 1

Step-by-step explanation:

1. Formula method =

$x = \frac{ - b + - \sqrt{ {b}^{2} - 4ac } }{ 2a}$

2. factorization method

3. completing square method

above are the methods for solving a quadratic equation.

Answer 2

Concept

A quadratic equation is an algebraic equation of degree two in the variable x. ax² + bx + c = 0 is the quadratic equation in standard form, where a and b represent the coefficients, x represents the variable, and c represents the constant term. A non-zero term (a 0) for the coefficient of x² is a prerequisite for an equation to be a quadratic equation.

Given

quadratic equations

Find

we need to find out the names of the methods used for solving a quadratic equation.

Solution

A quadratic equation can be solved in four different ways.

1) Factorizing the equation: The easiest technique to solve a quadratic equation if there are real, rational solutions is frequently to factorise it into the form (px + q)(mx + n), where m, n, p, and q are all integers. This is particularly true in cases where the value of x² is 1.

ex : x²+7x+12=0

We need two values that can be factored that sum up to 12 and multiply by two to produce 7. We obtain x²+7x+12=(x+3)(x+4)=0 because this is 3 and 4. Now that we have two brackets that add up to 0, we must find solutions when each of these brackets equals 0. Therefore, x=3 and x=4 are our solutions.

2) Principle of square root.

Place the square on one side and the constant on the other if the quadratic equation only contains a square and a constant (no first degree term). then calculate both sides' square root.

ex : x²₋16 = 0

x² = 16

x = ±√16

x = ₊4, 4

3) completing the square.

Try completing the square if the quadratic expression cannot be factored and the quadratic equation is of the type ax₊bx₊c where a ≠ 0

4) use the quadratic formula:

The quadratic formula can be used to find real and fictitious solutions to any quadratic equation of the type ax ₊ bx ₊ c where a≠0:

x = ₋b±√b²₋4ac/2a

hence we derive the four methods to solve the quadratic equation.

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