Question

Consider the quadratic equation \[ x^2+ax+b=0, \] where \(a,b\in\{1,2,3,4\}\). What is the probability that the equation has real roots?

• A. \(\dfrac{9}{16}\)
• B. \(\dfrac{5}{16}\)
• C. \(\dfrac{7}{16}\)
• D. \(\dfrac{3}{8}\)

Hint:

For a quadratic equation \[ ax^2+bx+c=0, \] the roots are real if \[ \boxed{b^2-4ac\ge0.} \] Here, \[ x^2+ax+b=0 \] so the discriminant is \[ \boxed{a^2-4b.} \]

Answer 1

The Correct Option is C