Question

The sign of the quadratic polynomial $a{x}^2+bx+c$ is always positive, if?

• A. a is positive and $b^2-4ac\le 0$
• B. a is positive and $b^2-4a\ge 0$
• C. a can be any real number and $b^2-4ac\le 0$
• D. a can be any real number and $b^2-4ac\ge 0$

Answer 1

The correct option is A a is positive and $b^2-4ac\le 0$

$a{x}^2+bx+c$ is always positive, if there exists no real root of the equation & $a$ is positive , $\Rightarrow$ The curve represented by above equation will never cut $x-axis$ and will be above it,

The condition for real root is $b^2-4ac<0$

If we apply the strict inequality we have $b^2-4ac\le 0$

$=b^2-4ac\le 0$ & ${}^{\prime }{a}^{\prime }$ is positive