Question : What is the value of m in the quadratic equation $x^{2}+mx+24=0$, if one of its roots is $\frac{3}{2}$.
Option 1: $–\frac{45}{2}$
Option 2: $16$
Option 3: $–\frac{21}{2}$
Option 4: $–\frac{35}{2}$
Correct Answer: $–\frac{35}{2}$
Solution : Given: $x^{2}+mx+24=0$ One of its roots is $\frac{3}{2}$. Putting $x=\frac{3}{2}$ into the equation, we have, $(\frac{3}{2})^{2}+m(\frac{3}{2})+24=0$ ⇒ $\frac{9}{4}+\frac{3m}{2}+24=0$ ⇒ $\frac{3m}{2}=–(\frac{9+96}{4})$ ⇒ $m=–\frac{105}{4}×\frac{2}{3}$ ⇒ $m=–\frac{35}{2}$ Hence, the correct answer is $–\frac{35}{2}$.
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