If the coefficints of x³ and x⁴ in the expansion of (1 + ax + b x²)(1 - 2x)¹⁸ in powers of x are both zero, then (a, b) is equal to:

Binomial Theorem and Its Simple Applications: JEE Main 2014 Mathematics question

JEE Main 2014 · Session, Shift 1 · Q2973

JEE Main 2014Session, Shift 1MathematicsMediumBinomial Theorem and Its Simple Applications131× since 2002

If the coefficints of

{x^3}

and

{x^4}

in the expansion of

\left( {1 + ax + b{x^2}} \right){\left( {1 - 2x} \right)^{18}}

in powers of

x

are both zero, then

\left( {a,\,b} \right)

is equal to: