The expression $ax^{2} + bx + c$ (where $a, b,$ and $c$ are real numbers) has the same sign as that of $a$ for all $x \in \mathbb{R}$ if:

  • A
    $b^{2} - 4ac > 0$
  • B
    $b^{2} - 4ac \neq 0$
  • C
    $b^{2} - 4ac < 0$
  • D
    $b$ and $c$ have the same sign as that of $a$

Explore More

Similar Questions

Number of equations of the form $ax^2 + bx + 1 = 0$ having real roots,where $a, b \in \{1, 2, 3, 4\}$ is-

The roots of the quadratic equation $x^2 - 2\sqrt{3}x - 22 = 0$ are:

If the roots of the equation $x^2 - 8x + a^2 - 6a = 0$ are real,then what is the range of $a$?

Difficult
View Solution

If $x^2+x-6$ is a factor of $2x^3+x^2+ax+b$,then $6a+13b=$

If $3$ is a root of the equation $x^2 + kx - 24 = 0$,then $3$ is also a root of which of the following equations?

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo