Question 357829
a)Use the discriminant.
{{{D=b^2-4ac}}}
{{{D=3^2-4(1)(k-1)}}}
For equal roots, 
{{{D=0}}}
{{{9-4(k-1)=0}}}
{{{4(k-1)=9}}}
{{{k-1=9/4}}}
{{{k=9/4+4/4}}}
{{{k=13/4}}}
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b) Use the quadratic formula,
{{{x = (-3 +- sqrt( 9-4(k-1) ))/(2)=-3 }}} 
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{{{-3 +- sqrt( 9-4(k-1) ))=-6 }}}
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{{{0 +- sqrt( 9-4(k-1) ))=-3 }}}
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{{{sqrt( 9-4(k-1) ))=3 }}}
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{{{ 9-4(k-1)=9 }}}
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{{{-4(k-1)=0}}}
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{{{highlight(k=1)}}}
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{{{x^2+3x=0}}}
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{{{drawing(300,300,-5,2,-3,3,circle(0,0,0.18),circle(-3,0,0.18),graph(300,300,-5,2,-3,3,x^2+3x))}}}