Multiple choice

If a,b,c >0 and $a=2b+3c$, then the roots of the equation $ax^2+bx+c=0$ are real if

  1. $\mid{\dfrac{a}{c}-11}\mid\geq4\sqrt{7}$
  2. $\mid{\dfrac{c}{a}-11}\mid>3\sqrt{7}$
  3. $\mid{\dfrac{b}{c}-4}\mid\geq4\sqrt{7}$
  4. $\mid{\dfrac{c}{b}-4}\mid\geq2\sqrt{7}$
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A Correct answer
Explanation

For real roots, the discriminant D = b^2 - 4ac >= 0. Substituting a = 2b + 3c into the inequality and rearranging leads to the condition involving the ratio of coefficients.

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