Q57 / 155 · WBJEE 2020 · Mathematics

The expression $a x^{2}+b x+c(a, b$ and $c$ are real $)$ has the same sign as that of a for all $x$ if

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

Solution

Hint: C-l: If $a>0, a x^{2}+b x+c>0, b^{2}-4 a c < 0, \quad C-I I:$ If $a \leq 0, a x^{2}+b x+c \leq 0, D \leq 0$

Hence, the correct answer is option: 'C'.

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