Solve = x²+250x-375000=0
Answers
Answer:
The first term is, x2 its coefficient is 1 .
The middle term is, +250x its coefficient is 250 .
The last term, "the constant", is -375000
Step-1 : Multiply the coefficient of the first term by the constant 1 • -375000 = -375000
Step-2 : Find two factors of -375000 whose sum equals the coefficient of the middle term, which is 250 .
-375000 + 1 = -374999
-187500 + 2 = -187498
-125000 + 3 = -124997
-93750 + 4 = -93746
-75000 + 5 = -74995
-62500 + 6 = -62494
-46875 + 8 = -46867
-37500 + 10 = -37490
-31250 + 12 = -31238
-25000 + 15 = -24985
-18750 + 20 = -18730
-15625 + 24 = -15601
-15000 + 25 = -14975
-12500 + 30 = -12470
-9375 + 40 = -9335
-7500 + 50 = -7450
-6250 + 60 = -6190
-5000 + 75 = -4925
-3750 + 100 = -3650
-3125 + 120 = -3005
-3000 + 125 = -2875
-2500 + 150 = -2350
-1875 + 200 = -1675
-1500 + 250 = -1250
-1250 + 300 = -950
-1000 + 375 = -625
-750 + 500 = -250
-625 + 600 = -25
-600 + 625 = 25
-500 + 750 = 250 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -500 and 750
x2 - 500x + 750x - 375000
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-500)
Add up the last 2 terms, pulling out common factors :
750 • (x-500)
Step-5 : Add up the four terms of step 4 :
(x+750) • (x-500)
Which is the desired factorization
Equation at the end of step
1
:
(x + 750) • (x - 500) = 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.