24d²-14d+2
pls answer with explanation
Answers
Answer:
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Answer :
D= -1/12,
or
D= -1/12
Step-by-step explanation:
STEP
1
:
Equation at the end of step 1
((23•3d2) + 14d) + 1 = 0
STEP
2
:
Trying to factor by splitting the middle term
2.1 Factoring 24d2+14d+1
The first term is, 24d2 its coefficient is 24 .
The middle term is, +14d its coefficient is 14 .
The last term, "the constant", is +1
Step-1 : Multiply the coefficient of the first term by the constant 24 • 1 = 24
Step-2 : Find two factors of 24 whose sum equals the coefficient of the middle term, which is 14 .
-24 + -1 = -25
-12 + -2 = -14
-8 + -3 = -11
-6 + -4 = -10
-4 + -6 = -10
-3 + -8 = -11
-2 + -12 = -14
-1 + -24 = -25
1 + 24 = 25
2 + 12 = 14 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 2 and 12
24d2 + 2d + 12d + 1
Step-4 : Add up the first 2 terms, pulling out like factors :
2d • (12d+1)
Add up the last 2 terms, pulling out common factors :
1 • (12d+1)
Step-5 : Add up the four terms of step 4 :
(2d+1) • (12d+1)
Which is the desired factorization
Equation at the end of step
2
:
(12d + 1) • (2d + 1) = 0
STEP
3
:
Theory - Roots of a product
3.1 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:
3.2 Solve : 12d+1 = 0
Subtract 1 from both sides of the equation :
12d = -1
Divide both sides of the equation by 12:
d = -1/12 = -0.083
Solving a Single Variable Equation:
3.3 Solve : 2d+1 = 0
Subtract 1 from both sides of the equation :
2d = -1
Divide both sides of the equation by 2:
d = -1/2 = -0.500