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Find the roots of rhe quadratic equation Root 5x^-9x+4 roots 5 =0 by factorization method?
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Find the roots of rhe quadratic equation Root 5x^-9x+4 roots 5 =0 by f...
Factorization Method for Finding Roots of Quadratic Equation
One of the most commonly used methods for finding the roots of a quadratic equation is the factorization method. This method involves factoring the quadratic equation into two linear factors and then setting each factor equal to zero to find the roots.
Step-by-Step Solution
Let's use the factorization method to find the roots of the quadratic equation:
5x² - 9x + 4 = 0
Step 1: Identify the Values of a, b, and c
For the quadratic equation ax² + bx + c = 0, the values of a, b, and c are:
- a = 5
- b = -9
- c = 4
Step 2: Find the Product and Sum of the Roots
The product and sum of the roots of a quadratic equation ax² + bx + c = 0 can be found using the following formulas:
- Product of roots = c/a
- Sum of roots = -b/a
Using the values of a, b, and c from step 1, we get:
- Product of roots = c/a = 4/5
- Sum of roots = -b/a = 9/5
Step 3: Find the Linear Factors
We now need to find two linear factors that multiply to give the quadratic expression:
5x² - 9x + 4
One way to do this is to use the product-sum method:
- Find two numbers that multiply to give the product of the roots (4/5) and add to give the sum of the roots (9/5).
- These two numbers are 4/5 and 1.
- Split the middle term -9x into -4x - 5x.
- Factor by grouping: 5x² - 4x - 5x + 4
- Factor out the GCF from the first two terms: x(5x - 4)
- Factor out the GCF from the last two terms: -1(5x - 4)
- Combine the two factors: (x - 4/5)(5x - 4)
Step 4: Set Each Factor Equal to Zero
Now that we have the two linear factors, we can set each one equal to zero and solve for x:
- x - 4/5 = 0
- 5x -
Community Answer
Find the roots of rhe quadratic equation Root 5x^-9x+4 roots 5 =0 by f...
Miss ...princesssss u have ask not completed question (it's my thought)!!! ur comple question is 5x^2-9x+4 root 5=0
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Find the roots of rhe quadratic equation Root 5x^-9x+4 roots 5 =0 by factorization method?
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Find the roots of rhe quadratic equation Root 5x^-9x+4 roots 5 =0 by factorization method? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Find the roots of rhe quadratic equation Root 5x^-9x+4 roots 5 =0 by factorization method? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the roots of rhe quadratic equation Root 5x^-9x+4 roots 5 =0 by factorization method?.
Find the roots of rhe quadratic equation Root 5x^-9x+4 roots 5 =0 by factorization method? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Find the roots of rhe quadratic equation Root 5x^-9x+4 roots 5 =0 by factorization method? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the roots of rhe quadratic equation Root 5x^-9x+4 roots 5 =0 by factorization method?.
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