Question

for what values of m the equations 3x^2+4mx+2=0 and 2x^2+3x-2=0 will have common root

Answer 1

Answer:

$value \:of \:m = \frac{7}{4}\:Or \:m =\frac{-11}{8}$

Step-by-step explanation:

$Given \: 3x^{2}+4mx+2=0\\and\:2x^{2}+3x-2=0\:have \\common \:root$

$i) Find \: roots \: of \:2x^{2}+3x-2=0$

/* Splitting the middle term,we get

$\implies 2x^{2}+4x-1x-2=0$

$\implies 2x(x+2)-1(x+2)=0$

$\implies (x+2)(2x-1)=0$

$\implies x+2=0\:Or\:2x-1=0$

$\implies x=-2\:Or\:2x=1$

$\implies x=-2\:Or\:x=\frac{1}{2}$

$Now,\\substitute\:x \: values\\in \:3x^{2}+4mx+2=0,we\:get$

$Case\:1\\if\:x=-2,\\\implies 3\times \big(-2)^{2}+4m(-2)+2=0$

$\implies 12-8x+2=0$

$\implies 14-8x=0$

$\implies -8x=-14$

$\implies x = \frac{-14}{-8}$

$\implies x = \frac{7}{4}$

$Case \:2\\If\:x=\frac{1}{2}$

$\implies 3\times \big(\frac{1}{2}\big)^{2}+4m\times \big(\frac{1}{2}\big)+2=0$

$\implies \frac{3}{4}+2m+2=0$

$\implies \frac{3+8m+8}{4}=0$

$\implies 11+8m=0$

$\implies 8m = -11$

$\implies m = \frac{-11}{8}$

$\implies m = \frac{-11}{8}$

Therefore,.

$value \:of \:m = \frac{7}{4}\:Or \:m =\frac{-11}{8}$

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Answer 2

Step-by-step explanation:

Hope it is helpful ❤️❤️