The answer is......... 27
Step-by-step explanation:
The quadratic equation is x² + (p - 5)x + 2q = 0.
By Vieta's Formula,
we have SOR = -b/a and POR = c/a.
=> (-3) + (6) = -(p - 5) and (-3)(6) = 2q.
=> 3 = 5 - p and -18 = 2q
Hence, p = 2 and q = -9.
Alternate Method:
We have (x + 3) and (x - 6) as factors of the quadratic equation x² + (p - 5)x + 2q = 0.
=> (x + 3)(x - 6) = x² - 3x - 18.
By Comparing Coefficients,
(p - 5) = -3 and 2q = 18.
Hence p = 2 and q = -9.
Answer:
a) Эx ∈ R ⊇ x³ = 2
b) ∀x ∈ R, x² ≥ 0
c) Эx ∈ R ⊇ x³ = x
d) ∀x ∈ R, x ≤ x²
Step-by-step explanation:
Given the data in the question;
let us first go through some symbols and their possible meanings;
Э ⇒ there exists
∀ ⇒ for all
∈ ⇒ belongs to or set membership or element of the set
⊇ ⇒ such that
now;
a) There is a number whose cube is equal to 2
let x represent the number; so
Эx ∈ R ⊇ x³ = 2
b) The square of every number is at least 0
x² ≥ 0, ∀x ∈ R
∀x ∈ R, x² ≥ 0
c) There is a number that is equal to its square
Эx ∈ R ⊇ x³ = x
d) Every number is less than or equal to its square.
x ≤ x², ∀x ∈ R
∀x ∈ R, x ≤ x²
Given that a line passes through the point (3,−7) and has a slope of −43. − 4 3 . Hence, the equation of the given line is 4x+3y+9=0.
