Question

If (x - 1) and (x + 2) are two factors of the polynomial 2x^3 + mx^2 - x - n, then the value of (m^2 - n^2) is​

Answer 1

Solution

Given :-

• Polynomial, 2x³ + mx² - x - n = 0
• (x -1) & (x+2) are factor of this equation,

Find :-

• Value of m² - n²

Explanation

we Know, if (x+a) is a factor of ax² + bx +c =0 . Then x = -a satisfied this equation

So,Here,

x = 1 & -2 Satisfied of this equation

Case(1).

Keep Value of x = 1 in this equation

➩ 2 * 1³ + m*(1)² - 1 - n = 0

➩ 2 + m - 1 - n = 0

➩ m - n = -1 -----------(1)

Case(2).

Keep Value of x = -2 in this equation

➩ 2 * (-2)³ + m*(-2)² - (-2) - n = 0

➩ -16 + 4m + 4 - n = 0

➩ 4m - n = 12 ----------(2)

Subtract equ(1) & equ(2)

➩ m - 4m = -1 - 12

➩ -3m = -13

➩ m = -13/(-3)

➩ m = 13/3

Keep Value of m in equ(1)

➩ 13/3 - n = -1

➩ n = 13/3 + 1

➩ n = (13+3)/3

➩ n = 16/3

Hence

• Value of m = 13/3
• Value of n = 16/3

________________

Answer Verification

Keep Value of m & n in equ(1)

➩ (13/3 - 16/3) = -1

➩ (13 - 16)/3 = -1

➩ -3/3 = -1

➩ -1 = -1

L.H.S. = R.H.S.

That's Proved.

_____________________

Now, Calculate Value of (m² - n²)

Keep Value of m & n

➩ (13/3)² - (16/3)²

➩ 169/9 - 256/9

➩(169-256)/9

➩ 87/9 [ Ans]

________________

Answer 2

Answer:

87/9 is the answer

Step-by-step explanation:

hope it will help you