Question

The approximation to a root of the equation x² + x - 1 = 0 in the interval (0, 1) by applying method of false position one time, will be:
1. 0.75
2. 0.5
3. 0.25
4. 0.65

Answer 1

Correct Answer - Option 2 : 0.5

Concept:

Regula-falsi method:

Considering, f(x) = 0

If f(a)×f(b) < 0, then the iterative formula is,

\({x_i} = \frac{{af\left( b \right) - bf\left( a \right)}}{{f\left( b \right) - f\left( a \right)}}\)

Important Points:

• The falsi position method is guaranteed to converge.
• The convergence is slow as it is first-order convergent.
• It is not necessarily a monotonic convergence to the root but most often it will be superior to the bisection method.

Calculation:

Given:

f(x) = x2 + x - 1

Taking a = 0 and  b = 1, we have

f(0) = -1 and f(1) = 1, so

\({x_1} = \frac{{0\times f\left( 1 \right) - 1\times f\left( 0 \right)}}{{f\left( 1 \right) - f\left( 0 \right)}}\)

x₁ = 0.5

Hence the required first approximation of the root will be 0.5.