Find the Roots of x2-21x+54
Answers
Answer:
2x-21x+54
2x (3×7) +(3×18)
2x 7 + 18
2x 25
x=12.5
x2-21x+54=0
Two solutions were found :
x = 18
x = 3
Step by step solution :
Step 1 :
Trying to factor by splitting the middle term
1.1 Factoring x2-21x+54
The first term is, x2 its coefficient is 1 .
The middle term is, -21x its coefficient is -21 .
The last term, "the constant", is +54
Step-1 : Multiply the coefficient of the first term by the constant 1 • 54 = 54
Step-2 : Find two factors of 54 whose sum equals the coefficient of the middle term, which is -21 .
-54 + -1 = -55
-27 + -2 = -29
-18 + -3 = -21 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -18 and -3
x2 - 18x - 3x - 54
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-18)
Add up the last 2 terms, pulling out common factors :
3 • (x-18)
Step-5 : Add up the four terms of step 4 :
(x-3) • (x-18)
Which is the desired factorization
Equation at the end of step 1 :
(x - 3) • (x - 18) = 0
Step 2 :
Theory - Roots of a product :
2.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
Solving a Single Variable Equation :
2.2 Solve : x-3 = 0
Add 3 to both sides of the equation :
x = 3
Solving a Single Variable Equation :
2.3 Solve : x-18 = 0
Add 18 to both sides of the equation :
x = 18
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