For the quadratic equation \(5x^2-4x+t=0\) to have real and equal roots, what is the value of \(t\)?

Correct answer: \(\frac{4}{5}\)

For a quadratic equation \(ax^2+bx+c=0\) to have real and equal roots, its discriminant must be zero: \(D=b^2-4ac=0\). Here, \(a=5\), \(b=-4\), and \(c=t\), so \((-4)^2-4(5)t=16-20t=0\). Therefore, \(t=\frac{4}{5}\). Option B results from reversing the numerator and denominator. Exam tip: whenever roots are real and equal, immediately use \(D=0\).