Ravi likes the number 17. His favorite polynomials are monotonic quadratics with integer coefficients such that 17 is a root of the quadratic and the roots differ by less than 17. Compute the sum of the coefficients of all of Ravi's favorite polynomials .(A monotonic quadratic is a quadratic polynomial whose x2 term has a coefficient if 1)
Hi Shivanshi,
Let the quadratic equation be (x-a)(x-b) = 0
Given, a = 17
We can find sum of the coefficients by substituting x with 1, i.e.
Sum of coefficients = (1-a)(1-b)
As it is mentioned that roots differ by less than 17, b can take values from 1 to 33
Required sum = (1-17)(1-1) + (1-17)(1-2) + ............ + (1-17)(1-33) = (16)(16)(33) = 8448
Hope this helps!
