If the roots of the equation $4 x^3-12 x^2+11 x+m=0$ are ir arithmetic progression, then $m=$

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Aicharya · Accepted Answer

$4 x^3-12 x^2+11 x+m=0$
Let the roots be $A-d, A, A+d$ $3 A=3 \Rightarrow A=1$ and roots are $1-d, 1,1+d$ $\begin{aligned} & 1-d+1+d+1-d^2=\frac{11}{4} \Rightarrow d= \pm \frac{1}{2} \\ & \text { Product of roots }=\frac{1}{2} \times 1 \times \frac{3}{2} \Rightarrow \frac{3}{4}=\frac{-m}{4} \Rightarrow m=-3 \end{aligned}$

If the roots of the equation $4 x^3-12 x^2+11 x+m=0$ are ir arithmetic progression, then $m=$

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