The solution of D2-5D+6y=0 is
Answers
Answer:
Factoring d2-5d+6
The first term is, d2 its coefficient is 1 .
The middle term is, -5d its coefficient is -5 .
The last term, "the constant", is +6
Step-1 : Multiply the coefficient of the first term by the constant 1 • 6 = 6
Step-2 : Find two factors of 6 whose sum equals the coefficient of the middle term, which is -5 .
-6 + -1 = -7
-3 + -2 = -5 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -3 and -2
d2 - 3d - 2d - 6
Step-4 : Add up the first 2 terms, pulling out like factors :
d • (d-3)
Add up the last 2 terms, pulling out common factors :
2 • (d-3)
Step-5 : Add up the four terms of step 4 :
(d-2) • (d-3)
Which is the desired factorization
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.
Solve : y = 0
Solution is y = 0
Solve : d-2 = 0
Add 2 to both sides of the equation :
d = 2
Solving d2-5d+6 = 0 directly
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