Question

anyone can explain quadratic equation with examples.

Answer 1

A standard quadratic equation looks like this:

ax2+bx+c = 0

Where a, b, c are numbers and a≥1.

a, b are called the coefficients of x2 and x respectively and c is called the constant.

 

The following are examples of some quadratic equations:

1) x2+5x+6 = 0 where a=1, b=5 and c=6.

2) x2+2x-3 = 0 where a=1, b=2 and c= -3

3) 3x2+2x = 1

→ 3x2+2x-1 = 0 where a=3, b=2 and c= -1

4) 9x2 = 4

→ 9x2-4 = 0 where a=9, b=0 and c= -4

 

For every quadratic equation, there can be one or more than one solution. These are called the roots of the quadratic equation.

For a quadratic equation ax2+bx+c = 0,

the sum of its roots = –b/a and the product of its roots = c/a.

A quadratic equation may be expressed as a product of two binomials.

For example, consider the following equation

x2-(a+b)x+ab = 0

x2-ax-bx+ab = 0

x(x-a)-b(x-a) = 0

(x-a)(x-b) = 0

x-a = 0 or x-b = 0
x = a or x=b

Here, a and b are called the roots of the given quadratic equation.

 

Now, let’s calculate the roots of an equation x2+5x+6 = 0.

We have to take two numbers adding which we get 5 and multiplying which we get 6. They are 2 and 3.

Let us express the middle term as an addition of 2x and 3x.

→ x2+2x+3x+6 = 0

→ x(x+2)+3(x+2) = 0

→ (x+2)(x+3) = 0

→ x+2 = 0       or         x+3 = 0

→ x = -2          or         x = -3

This method is called factoring.

We saw earlier that the sum of the roots is –b/a and the product of the roots is c/a. Let us verify that.

Sum of the roots for the equation x2+5x+6 = 0 is -5 and the product of the roots is 6.

The roots of this equation -2 and -3 when added give -5 and when multiplied give 6.

Answer 2

A standard quadratic equation looks like this:

ax2+bx+c = 0

Where a, b, c are numbers and a≥1.

a, b are called the coefficients of x2 and x respectively and c is called the constant.

 

The following are examples of some quadratic equations:

1) x2+5x+6 = 0 where a=1, b=5 and c=6.

2) x2+2x-3 = 0 where a=1, b=2 and c= -3

3) 3x2+2x = 1

→ 3x2+2x-1 = 0 where a=3, b=2 and c= -1

4) 9x2 = 4

→ 9x2-4 = 0 where a=9, b=0 and c= -4

 

For every quadratic equation, there can be one or more than one solution. These are called the roots of the quadratic equation.

For a quadratic equation ax2+bx+c = 0,

the sum of its roots = –b/a and the product of its roots = c/a.

A quadratic equation may be expressed as a product of two binomials.

For example, consider the following equation

x2-(a+b)x+ab = 0

x2-ax-bx+ab = 0

x(x-a)-b(x-a) = 0

(x-a)(x-b) = 0

x-a = 0 or x-b = 0
x = a or x=b

Here, a and b are called the roots of the given quadratic equation.

 

Now, let’s calculate the roots of an equation x2+5x+6 = 0.

We have to take two numbers adding which we get 5 and multiplying which we get 6. They are 2 and 3.

Let us express the middle term as an addition of 2x and 3x.

→ x2+2x+3x+6 = 0

→ x(x+2)+3(x+2) = 0

→ (x+2)(x+3) = 0

→ x+2 = 0       or         x+3 = 0

→ x = -2          or         x = -3

This method is called factoring.

We saw earlier that the sum of the roots is –b/a and the product of the roots is c/a. Let us verify that.

Sum of the roots for the equation x2+5x+6 = 0 is -5 and the product of the roots is 6.

The roots of this equation -2 and -3 when added give -5 and when multiplied give 6.

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