If (1 + Sqrt2) and (1 - Sqrt2) are the roots of the equation ax^2 + bx - 1 = 0, then find the values

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31 Mar 2016 Quadratic Equation

If (1 + Sqrt2) and (1 - Sqrt2) are the roots of the equation ax^2 + bx - 1 = 0, then find the values of a and b.

OPtion

1) Sqrt2, 1
2) -1, Sqrt2
3) -2, Sqrt2
4) 1, Sqrt2
5) 1, -2
6) 1, -3
7) 2, -1
8) 3, -1
9) -1, -2
10) 1, 2

Solution

Sum of roots = 1 + Sqrt2 + 1 - Sqrt2 = 2
Product of roots = (1 + Sqrt2)(1 - Sqrt2) = -1
Sum of roots = -b/a = 2
b = -2a
And product of roots = -1/a = -1
a = 1
b = -2
Option 5)

Correct Option: 5 Best Solution (7)