Question

A quadratic equation \[ x^2-ax+b=0,\qquad a>0 \] has real roots. If the sum of the roots is less than the product of the roots, then \(b\) lies in the interval

• A. \((4,\infty)\)
• B. \((-\infty,0)\cup(4,\infty)\)
• C. \((-\infty,1)\cup(2,\infty)\)
• D. \((1,3)\)

Hint:

For the quadratic equation \[ x^2-Sx+P=0, \] \[ \boxed{\text{Sum of roots}=S,\qquad \text{Product of roots}=P.} \] Always use the discriminant condition \[ \boxed{S^2-4P\ge0} \] when the roots are real.

Answer 1

The Correct Option is A