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cornpops1749
20.10.2020 •
Mathematics
<5 is a supplement of <6 and m <5=78. find m<6 <5 is a supplement of <6 and m<5=78. find m <6
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Ответ:
1.1 Factoring x2-16x+48
-48 + -1 = -49 -24 + -2 = -26 -16 + -3 = -19 -12 + -4 = -16 That's itThe first term is, x2 its coefficient is 1 .
The middle term is, -16x its coefficient is -16 .
The last term, "the constant", is +48
Step-1 : Multiply the coefficient of the first term by the constant 1 • 48 = 48
Step-2 : Find two factors of 48 whose sum equals the coefficient of the middle term, which is -16 .
Equation at the end of step 1 : (x - 4) • (x - 12) = 0 Step 2 :Theory - Roots of a product :Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -12 and -4
x2 - 12x - 4x - 48
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-12)
Add up the last 2 terms, pulling out common factors :
4 • (x-12)
Step-5 : Add up the four terms of step 4 :
(x-4) • (x-12)
Which is the desired factorization
2.1 A product of several terms equals zero.
Solving a Single Variable Equation :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.
2.2 Solve : x-4 = 0
Solving a Single Variable Equation :Add 4 to both sides of the equation :
x = 4
2.3 Solve : x-12 = 0
Supplement : Solving Quadratic Equation DirectlySolving x2-16x+48 = 0 directlyAdd 12 to both sides of the equation :
x = 12
Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula
Parabola, Finding the Vertex :3.1 Find the Vertex of y = x2-16x+48