Let f ( x ) = x 3 + a x 2 + b x + c be polynomial with integer coefficients. If the roots of f ( x ) are integer and are in Arithmetic Progression, then ' a ' cannot take the value

Question

Let f ( x ) = x 3 + a x 2 + b x + c be polynomial with integer coefficients. If the roots of f ( x ) are integer and are in Arithmetic Progression, then ' a ' cannot take the value, − 642, 1214, 1323, 1626

MARKS App · Accepted Answer

Given that, f ( x ) = x 3 + a x 2 + b x + c Now, since the roots of the polynomial are in Arithmetic Progression, Let the roots are s - t , s , s + t ⇒ s - t + s + s + t = - a 1 ⇒ - 3 s = a Hence, a must be multiple of 3 . From given options we see that only 1214 is not multiple of 3 .

Search any question & find its solution

Looking for more such questions to practice?