Question

Pls do the star marked question

Answer 1

here is your answer

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Answer 2

           

$p(x)=(m-12)x^2+2(m-12)x+2=0 \\ \\ \\ a=m-12 \\ \\ b=2(m-12) \\ \\ c=2$

$If \ p(x)\ has equal roots, then the discriminant shall be 0.$

$\Rightarrow\ b^2-4ac=0 \\ \\ \Rightarrow\ (2(m-12))^2-(4(m-12)2)=0 \\ \\ \Rightarrow\ (2m-24)^2-(8m-96)=0 \\ \\ \Rightarrow\ 4m^2-96m+576-8m+96=0 \\ \\ \Rightarrow\ 4m^2-104m+672=0 \\ \\ \Rightarrow\ 4m^2-48m-56m+672=0\\ \\ \Rightarrow\ 4m(m-12)-56(m-12)=0\\ \\ \Rightarrow\ (4m-56)(m-12)=0 \\ \\ \Rightarrow\ 4(m-14)(m-12)=0 \\ \\ \\ \therefore\ m=\bold{14}\ \ \ \ \ OR \ \ \ \ \ m=\bold{12}$

$But,\ in \ p(x)=(m-12)x^2+2(m-12)x+2=0,\ \\ \\ if we take \ m=12,\ the coefficient of \ x^2\ will be 0. \\ \\ \\ We know that the coefficient of \ x^2\ in a quadratic equation shall not be 0. \\ \\ \\ \therefore\ We can't take \ m=12. \\ \\ \\ \therefore\ m=\bold{14}$

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