2016 · Q8
In the quadratic equation x²+ax+b=0, a and b can take any value from the set {1, 2, 3, 4}. How many pairs of values of a and b are possible in order that the quadratic equation has real roots ?
Elementary MathematicsAlgebra
- A6
- B7
- C8
- D16
Explanation
Real roots need discriminant a²−4b ≥ 0. For a=1: no b works; a=2: b=1 (1 pair); a=3: b=1,2 (2 pairs); a=4: b=1,2,3,4 (4 pairs). Total 1+2+4 = 7 pairs (option B).