How do you factorize 2x2 + 3x + 1?
Last Updated :
30 Dec, 2023
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- am×an=am+n.
- When the exponent has another exponent, the base remains the same but the powers are multiplied. For eg- (am)n=am×n.
- To divide two exponential numbers with the same bases, the exponents are subtracted and the base remains the same. For eg- am/an=am-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.
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