Question

If y = 2x³ – 3x² + 3x – 10, the value of Δ³y will be (where, Δ is forward differences operator)
1. 10
2. 11
3. 12
4. 13

Answer 1

Correct Answer - Option 3 : 12

Concept:

If f(x) = a₀xⁿ + a₁x^n-1 + a₂x^n-2 + … a_n is a polynomial of degree ‘n’, then

\({{\rm{\Delta }}^n}f\left( x \right) = \left[ {\left( {n!} \right) \cdot h \cdot {a_0}} \right]\;\& \;{{\rm{\Delta }}^{n + r}}f\left( x \right) = 0\;for\;r = 1,\;2,\;3 \ldots\)

Where h is the step size

Calculation:

Given polynomial is y = 2x³ – 3x² + 3x – 10 & we have to calculate Δ³y where Δ is forward difference operator.

So Δ³y = (n!) (a₀)(h) = (3!)⋅(2)h = 12h

⇒ Δ²y = 12h

Step size = 1 {since it is not given so take it as 1}

⇒ Δ²y = 12