Question

•15. Find a and ß, if x + 1 and x + 2 are factors of x + 3x2 - 2ax +B.​

Answer 1

$\sf{\huge{\underline{\green{Correct \:Question :-}}}}$

• Find α and ß, if x + 1 and x + 2 are factors of x + 3x²- 2αx + 2β.

$\sf{\huge{\underline{\green{Given :-}}}}$

• x + 1 and x + 2 are factors of x + 3x² - 2αx +2β.

$\sf{\huge{\underline{\green{To\:Find :-}}}}$

• The value of α and ß .

$\sf{\huge{\underline{\green{Answer :-}}}}$

According to the question,

(x + 1) and (x + 2) are the factors of x + 3x2 - 2αx + 2β.

• (x + 1) = 0

➝ x = -1

• (x + 2) = 0

➝ x = -2

x + 3x²- 2αx + 2β = 0

For, x = -1

(-1)³ + 3(-1)² - 2α(-1) + 2β =0

-1 + 3 - (- 2α) + 2β = 0

-1 + 3 + 2α + 2β = 0

2 + 2α + 2β = 0

2α + 2β = -2

2(α + β) = -2

(α + β) = -2/2

α + β = -1 -----(1)

x³ + 3x² - 2αx + 2β = 0

For, x = -2

(-2)³ + 3(-2)² - 2(-2)a + 2B = 0

-8 + 3(4) - (- 4α) + 2β = 0

-8 + 12 + 4 α + 2β = 0

4 + 4α + 2β = 0

4α + 2β = 4

2(2α + β) = 4

(2α + β) = 4/2

2α + β = 2 -----(2)

Subtract eq(2) from (1)

α + β = -1 -----(1)

2α + β = 2 -----(2)

- - -

____________

-α = 1

____________

α = -1

-1 + β = -1

β = -1 + 1

β = 0