Question

ax² + bx + c = 0, a > 0,b = 0, c > 0 has; 

A) Two equal roots 

B) One real root 

C) Two distinct real roots 

D) No real roots

Answer 1

Correct option is (D) No real roots

\(ax^2+bx+c=0\)

\(\because\) b = 0                     (Given)

\(\Rightarrow ax^2+c=0\)

\(\because\) a > 0 & c > 0         (Given)

& \(x^2>0\)

\(\therefore ax^2>0\) & c > 0          \((\because\) Product of two positive numbers is always positive)

\(\Rightarrow ax^2+c>0\)               \((\because\) Sum of two positive numbers is always positive)

Then it has no real roots.

Hence, \(ax^2+bx+c=0,\) b = 0, a, c > 0 has no real roots.

Answer 2

Correct option is D) No real roots