Q53 / 160 · AP EAMCET 2024 (21 May Shift 1) · Mathematics
If the roots of the equation $4 x^3-12 x^2+11 x+m=0$ are ir arithmetic progression, then $m=$
- Correct answerA-3
- B1
- C2
- D3
Solution
$4 x^3-12 x^2+11 x+m=0$
Let the roots be $A-d, A, A+d$ $3 A=3 \Rightarrow A=1$ and roots are $1-d, 1,1+d$ $\begin{aligned} & 1-d+1+d+1-d^2=\frac{11}{4} \Rightarrow d= \pm \frac{1}{2} \\ & \text { Product of roots }=\frac{1}{2} \times 1 \times \frac{3}{2} \Rightarrow \frac{3}{4}=\frac{-m}{4} \Rightarrow m=-3 \end{aligned}$
Let the roots be $A-d, A, A+d$ $3 A=3 \Rightarrow A=1$ and roots are $1-d, 1,1+d$ $\begin{aligned} & 1-d+1+d+1-d^2=\frac{11}{4} \Rightarrow d= \pm \frac{1}{2} \\ & \text { Product of roots }=\frac{1}{2} \times 1 \times \frac{3}{2} \Rightarrow \frac{3}{4}=\frac{-m}{4} \Rightarrow m=-3 \end{aligned}$
Hence, the correct answer is option: 'A'.