For which value will ((a+6)x-13) not remain a linear polynomial?

Correct answer: \(a=-6\)

For a polynomial to be linear, the coefficient of \(x\) must be non-zero. Here, the coefficient of \(x\) is \(a+6\). On putting \(a=-6\), we get \(a+6=0\), so the expression becomes \(-13\), a constant polynomial rather than a linear polynomial. For example, when \(a=0\), the expression is \(6x-13\), which is still linear. Exam tip: In parameter-based polynomials, first check when the coefficient of the highest-power term becomes zero.