find the zeroes of polynomial 2x²-13x-34
Answers
Answer:
Step-by-step explanation:
STEP
1
:
Equation at the end of step 1
(2x2 - 13x) - 34 = 0
STEP
2
:
Trying to factor by splitting the middle term
2.1 Factoring 2x2-13x-34
The first term is, 2x2 its coefficient is 2 .
The middle term is, -13x its coefficient is -13 .
The last term, "the constant", is -34
Step-1 : Multiply the coefficient of the first term by the constant 2 • -34 = -68
Step-2 : Find two factors of -68 whose sum equals the coefficient of the middle term, which is -13 .
-68 + 1 = -67
-34 + 2 = -32
-17 + 4 = -13 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -17 and 4
2x2 - 17x + 4x - 34
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (2x-17)
Add up the last 2 terms, pulling out common factors :
2 • (2x-17)
Step-5 : Add up the four terms of step 4 :
(x+2) • (2x-17)
Which is the desired factorization
Equation at the end of step
2
:
(2x - 17) • (x + 2) = 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