Question

Aflati valorile parametrului real m, astfel incit ecuatia sa aiba o unica solutie.
b. x²+3mx+m=0

c. 2x²-2x+m=0

d. 9x²-2x+m=6-mx

Answer 1

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Answer 2

 [tex]ax^2+bx+c=0\;\;are\;solutie\;unica\;daca\;\Delta=0\;!\\ b)...\;in\,acest\,caz\;...\;a=1\;;\;b=3m\;si\;c=m\;\\ \Rightarrow\;\Delta=9m^2-4\cdot1\cdot{m}=9m^2-4m=m(9m-4) \Rightarrow\;m=\{0\;;\;\frac{4}{9}\}[/tex];
$c)...\Delta=2^2-4\cdot(-2)\cdot(m)=0\Leftrightarrow4+8m=0\;;\;\rightarrow{m}=-\frac{1}2}$
[tex]d)...9x^2-2x+mx+m-6=\underbrace{9x^2+(m-2)x+m-6=0}\\ \Delta=(m-2)^2-4\cdot9\cdot(m-6)=0 \;\\ \Rightarrow\;\Delta=m^2-4m+4-36m+216=0\,\,deci\,\,\Delta=m^2-40m+220=0\\ de \;unde\;\rightarrow\;m_1\;si\;m_2\;pt.care\; ecuatia\; are \;solutii\;unice\;![/tex]