anyone can explain quadratic equation with examples.
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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.
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.
nousheen47:
(2a + 1) (a+3) + 3 = 0 in this question
can you help me
thnkd
thnks
Answered by
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.
HOPE IT HELPS U ✌️✌️
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.
HOPE IT HELPS U ✌️✌️
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