What must be added to x² - 3x to make it a perfect square?

  • A \(\frac{9}{4}\)
  • B \(\frac{9}{2}\)
  • C 6
  • D 9
waec 2006mathematics

The correct answer is A. \(\frac{9}{4}\)

A perfect square trinomial is of the form \((a - b)^2 = a^2 - 2ab + b^2\).

Comparing this with \(x^2 - 3x\), we can see that \(a = x\) and \(2ab = 3x\). Solving for \(b\), we get \(b = \frac{3x}{2x} = \frac{3}{2}\).

The term that must be added to \(x^2 - 3x\) to make it a perfect square is \(b^2 = \left(\frac{3}{2}\right)^2 = \frac{9}{4}\).

Previous question Next question