Find α and β if x+1 and x+2 are factors of x³+3x²-2αx+β.
Answers
please mark it as a brainliest answer
Let, f (x) = x³ + 3x² - 2αx + β be the given polynomial.
From factor theorem, If (x + 1) and (x + 2) are factors of f (x) then f (-1) = 0 and f (-2) = 0 :
f (-1) = 0
⇒(-1)³ + 3 (-1)² - 2 α (-1) + β = 0
⇒ - 1 + 3 + 2 α + β = 0
⇒ 2 α + β + 2 = 0 ……………(1)
Similarly,
f (- 2) = 0
⇒ (-2)³ + 3 (- 2)² – 2α (- 2) + β = 0
⇒ - 8 + 12 + 4 α + β = 0
⇒ 4 α + β + 4 = 0 ……………(2)
Subtract eq (1) from eq (2) :
⇒ 4 α + β + 4 – (2 α + β + 2) = 0 - 0
⇒ 4 α + β + 4 - 2 α - β - 2 = 0
⇒ 4 α - 2 α + β - β + 4 - 2 = 0
⇒ 2 α + 2 = 0
⇒ 2 α = 0 - 2
⇒ 2 α = - 2
⇒ α = - 2/2
⇒ α = -1
On Putting α = -1 in eq (1) :
⇒ 2 α + β + 2 = 0
⇒ 2 (-1) + β + 2 = 0
⇒ - 2 + β + 2 = 0
⇒ β = 0
Hence, α = -1 and β = 0.
HOPE THIS ANSWER WILL HELP YOU…..
Similar questions :
For what value of a is (x-5) a factor of x³-3x²+ax-10.
brainly.in/question/15904221
Find the value of p and q if x4+px3+2x2-3x+q is divisible by x²-1
https://brainly.in/question/12308408