1.

If x = 1 and x = -1/3 are roots of the equation mx2 – nx – 1 = 0. Determine the value of m and n.  1. m = -3 and n = 2 2. m = 3 and n = -23. m = 2 and n = 2 4. m = 3 and n = 2

Answer» Correct Answer - Option 4 : m = 3 and n = 2 

Given:

Roots of quadratic equation are -1/3 and 1 

Calculation:

x = 1

m(1)2 – n(1) – 1 = 0

⇒ m – n -1 = 0

⇒ m – n = 1                                                  …………………….. (1)

x = -1/3

m(-1/3)2 – n(-1/3) – 1 = 0

⇒ m/9 + n/3 = 1

⇒ m + 3n = 9                                              ………………………. (2)

From equation (1) and (2)

-4n = -8

⇒ n = 2

Now,

⇒ m – 2 = 1

⇒ m = 3

∴ m = 3 and n = 2 

The correct option is 4 i.e. m = 3 and n = 2 


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