Find the value of k such that \(t^2\) + kt + \(\frac{25}{4}\) is a perfect…

Explanation

\(t^2\) + kt + \(\frac{25}{4}\)

The general form of quadratic expression = ax\(^2\) + bx + c

comparing  \(t^2\) + kt + \(\frac{25}{4}\) and the general form 

a = 1, b = k and c = \(\frac{25}{4}\)

using: b\(^2\) = 4ac we can find the value of k. ( note: there is/are another way(s) to find the value of k)

k\(^2\) = 4 x 1 x  \(\frac{25}{4}\)

k\(^2\) = 25

taking the square root of both sides

k = 5