How do you factorize 2x² + 3x + 1?

Exponents and powers are a method to express repeated multiplication of the same number. For eg- 5×5×5×5 can be written as 54 where is the base and 4 is the exponent. It is most commonly used to express the powers of 10 to write a very large number in a convenient manner. For eg- 1000 can be written as 10³.

Laws of Exponents

• To multiply two exponential numbers with the same bases, the exponents are added and the base remains the same. For eg- a^m×aⁿ=a^m+n.
• When the exponent has another exponent, the base remains the same but the powers are multiplied. For eg- (a^m)ⁿ=a^m×n.
• To divide two exponential numbers with the same bases, the exponents are subtracted and the base remains the same. For eg- a^m/aⁿ=a^m-n.

What is a Quadratic Equation?

The quadratic equations are 2-degree polynomial equations with one variable. The general form of a quadratic equation is given as f(x) = ax² + bx + c where a, b and c are real numbers and a≠0. In the general form, ‘a’ is the leading coefficient and ‘c’ is the absolute term. The values of x that satisfy the polynomial equation are known as the roots of the quadratic equation.

When a quadratic polynomial is equated to zero, it becomes a quadratic equation. The general form of the equation is ax² + bx + c = 0. 

For eg- 2x²+3x+6=0, 4x²+7x+3=0, x²+2x=0.

Quadratic Equation Formula

The roots or solution of a quadratic equation are calculated by the formula given below:

(α, β) = (-b±√(b²-4ac))/2a 

where, 

α and β are the roots of the equation.

Steps to solve a quadratic equation

Step 1: Write the quadratic equation and equate it to zero.

Step 2: Identify the values of ‘a’, ‘b’, and ‘c’ from the equation.

Step 3: Substitute the values in the quadratic equation formula and solve for the values of the roots.

Step 4: Make sure the calculation is correct.

How do you factor 2x² + 3x + 1?

Solution:

Given that the quadratic equation is 2x² + 3x + 1

Equate the quadratic equation to zero.

2x² + 3x + 1 = 0

Here, a = 2, b = 3 and c = 1.

Substitute the values in the quadratic equation formula.

x = (-3±√(3²-4×2×1))/2×2

x = (-3±√1)/4

x = (-3±1)/4

x = -1/2, -1

Hence, the factors of the equation as -1/2 and -1.

Similar Questions

Question 1: What are the factors of x² + 3x + 2?

Solution:

Given that the quadratic equation is x²+3x+2.

Equate the quadratic equation to zero.

x² + 3x + 2 = 0

Here, a = 1, b = 3 and c = 2.

Substitute the values in the quadratic equation formula.

x = (-3±√(3²-4×1×2))/2×1

x = (-3±√1)/2

x = (-3±1)/2

x = -1, -2

Hence, the factors of the equation as -1 and -2.

Question 2: What are the factors of x² + 7x + 12.

Solution:

Given that the quadratic equation is x² + 7x + 12.

Equate the quadratic equation to zero.

x² + 7x + 12 = 0

Here, a = 1, b = 7 and c = 12.

Substitute the values in the quadratic equation formula.

x = (-7±√(7²-4×1×12))/2×1

x = (-7±√1)/2

x = (-7±1)/2

x = -4, -3

Hence, the factors of the equation as -4 and -3.