Question

if alpha and beta are zeroes of a given polynomial f(x)=x*-p(x+2)-c then find the value of (alpha +2)(beta+2)

Answer 1

Answer:

Given:

alpha and beta are zeros

polynomial f(x)=x² -p(x+2)-c

To find:

the value of (α + 2)(β +2)

Solving Question:

We are given the polynomial and then asked to find the value of

(alpha +2)(beta+2) for that first we have to simplify the question and the given polynomial then it could be substituted in the equations

If α and β are the zeros,then,

α + β = -b/a

α * β = c/a

Solution:

first take polynomial

⇒ x² -p(x+2)-c

or, x² - px - 2p -c = 0

a = 1 , b = -1 , c = (-2p -c)

Then take the question,

(alpha +2)(beta+2)

⇒ (α +2) (β+2)

or, αβ +2α +2β +4

or, αβ + 2(α + β ) +4

α + β = -b/a

α * β = c/a

⇒ αβ + 2(α + β ) +4

or, c/a + 2(-b/a) +4

or, (-2p-c)/1 + 2(P)/1 + 4  [a = 1 , b = -1, c = (-2p -c) ]

or, -2p - c + 2p +4

or, 4-c

or, 4-c

∴ The value of (α + 2)(β +2) is  4-c