For what values of m, the equation (1+m)x2-2(1+3m)x+(1+8m)=0 has (m∈R) both roots are equal?

∵(1+m)x2−2(1+3m)x+(1+8m)=0∴D=4(1+3m)2−4(1+m)(1+8m)=4m(m−3)Both roots are equal.∴ D=0⇒4m(m−3)=0⇒m=0,3

For what values of m, the equation (1+m)x2-2(1+3m)x+(1+8m)=0 has (m∈R) both roots are equal?

∵(1+m)x2−2(1+3m)x+(1+8m)=0∴D=4(1+3m)2−4(1+m)(1+8m)=4m(m−3)Both roots are equal.∴ D=0⇒4m(m−3)=0⇒m=0,3

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For what values of m, the equation $(1 + m) x^{2} - 2 (1 + 3 m) x + (1 + 8 m) = 0 has (m \in R)$ both roots are equal?

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3, 5

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$\begin{array}{l} ∵ (1 + m) x^{2} - 2 (1 + 3 m) x + (1 + 8 m) = 0 \\ ∴ D = 4 (1 + 3 m)^{2} - 4 (1 + m) (1 + 8 m) = 4 m (m - 3) \end{array}$

Both roots are equal.

$\begin{array}{l} ∴ D = 0 \\ \Rightarrow 4 m (m - 3) = 0 \\ \Rightarrow m = 0, 3 \end{array}$

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For what values of m, the equation (1+m)x2-2(1+3m)x+(1+8m)=0 has (m∈R) both roots are equal?

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For what values of m, the equation $(1 + m) x^{2} - 2 (1 + 3 m) x + (1 + 8 m) = 0 has (m \in R)$ both roots are equal?