find the roots of the following quardratic equations by factorisation: 100x²-20x+1=0
Answers
- Roots are
- X = 1/10
Answer:
x = 1/10 = 0.100
Step-by-step explanation:
Step by Step Solution:
Step by step solution :
Step
1
:
Equation at the end of step 1
((22•52x2) - 20x) + 1 = 0
Step
2
:
Trying to factor by splitting the middle term
2.1 Factoring 100x2-20x+1
The first term is, 100x2 its coefficient is 100 .
The middle term is, -20x its coefficient is -20 .
The last term, "the constant", is +1
Step-1 : Multiply the coefficient of the first term by the constant 100 • 1 = 100
Step-2 : Find two factors of 100 whose sum equals the coefficient of the middle term, which is -20 .
-100
+
-1
=
-101
-50
+
-2
=
-52
-25
+
-4
=
-29
-20
+
-5
=
-25
-10
+
-10
=
-20
That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -10 and -10
100x2 - 10x - 10x - 1
Step-4 : Add up the first 2 terms, pulling out like factors :
10x • (10x-1)
Add up the last 2 terms, pulling out common factors :
1 • (10x-1)
Step-5 : Add up the four terms of step 4 :
(10x-1) • (10x-1)
Which is the desired factorization
Multiplying Exponential Expressions:
2.2 Multiply (10x-1) by (10x-1)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (10x-1) and the exponents are :
1 , as (10x-1) is the same number as (10x-1)1
and 1 , as (10x-1) is the same number as (10x-1)1
The product is therefore, (10x-1)(1+1) = (10x-1)2
Equation at the end of step
2
:
(10x - 1)2 = 0
Step
3
:
Solving a Single Variable Equation
3.1 Solve : (10x-1)2 = 0
(10x-1) 2 represents, in effect, a product of 2 terms which is equal to zero
For the product to be zero, at least one of these terms must be zero. Since all these terms are equal to each other, it actually means : 10x-1 = 0
Add 1 to both sides of the equation :
10x = 1
Divide both sides of the equation by 10:
x = 1/10 = 0.100