Question

If a and b can take values 1, 2, 3 and 4, then the number of equations of the form $a{x}^2+bx+1=0$ having real roots is _____.

• A. 10
• B. 6
• C. 7
• D. 12

Answer 1

The correct option is C

7

$a{x}^2+bx+1=0$ has real roots only if D ≥ 0 or $b^2-4ac\ge 0$.
Only 7 values of a and b satisfy it which is (1,2), (1,3), (1,4), (2,3), (2,4), (3,4) and (4,4).

For (a,b) = (1,2) $\Rightarrow D=(2{)}^2-4(1\left)\right(1)=0\ge 0$
For (a,b) = (3,4) $\Rightarrow D=(4{)}^2-4(3\left)\right(1)=4\ge 0$

This can be verified for the other values of a and b.