Answer:
q=35
Step-by-step explanation:
x2 - 12x + q = 0
Let the two roots be r and r+2.
Factor the quadratic expression:
(x - r)[x - (r + 2)] = 0
Expand, simplify, group like terms, and get
x2 - 2(r + 1)x + r(r + 2) = 0
Compare to
x2 - 12x + q = 0
and set equal the coefficients of like terms:
Coefficient of x:
-2(r + 1) = -12 ⇒ r + 1 = 6 ⇒ r = 5
(Then the other root is r + 2 = 5 + 2 = 7)
Constant term:
r(r + 2) = q ⇒ 5(5 + 2) = q
q = 35
Test the solution:
(x - 5)(x - 7) = x2 - 12x + 35
With two roots differing by 2, you get an equation of the form
x2 - 12x + q = 0
with q = 35.
Answer: Daniel is 13 years old; Ben is 33 years old
Step-by-step explanation:
Math
Answer:
revenue: $104 profit: $39
Step-by-step explanation:
Answer:
Step-by-step explanation:
P + 4.5 = - p + 5
Bringing like terms on one side
P + p = 5 - 4.5
2p = 0.5
p = 0.5/2 = 0.25
In my opinion the answer is one solution
Answer:
-5 is a root
Step-by-step explanation:
It would help to see any possible answers for this if this is a multiple choice question, but if a factor of f(x) is (x+5), then -5 must be a root of a function.
To find roots, set factor equal to zero and solve:
x + 5 = 0
x = -5
