Question 147659
a.)Let's call the amount invested at 4%, A, and
call the amount invested at 6.5%, B.
What do we know?
The total invested was $6000.
1.{{{A+B=6000}}}
After one year the total interest was $335.
2.{{{A(4/100)+B*(6.5/100)=335}}}
Let's multiply both sides of eq. 2 by 100 to get rid of denominators.
2.{{{4*A+6.5*B=33500}}}
Now we can use eq. 1 to get A in terms of B and substitute into eq. 2,
1.{{{A+B=6000}}}
{{{A=6000-B}}}
Now substitute into eq. 2,
2.{{{4*A+6.5*B=335000}}}
{{{4*(6000-B)+6.5*B=33500}}}
{{{(24000-4B)+6.5*B=33500}}}
{{{2.5*B=9500}}}
{{{B=3800}}}
From eq. 1,
{{{A=6000-B}}}
{{{A=6000-3800}}}
{{{A=2200}}}
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b1)3x2 – 4x + 7 = 0
The quadratic formula deals with an equation of the form,
{{{ax^2+bx+c=0}}}
in your case,
{{{a=3}}}
{{{b=-4}}}
{{{c=7}}}
The discriminant is,
{{{b^2-4ac=(-4)^2-4*3*7}}}
{{{b^2-4ac=16-84}}}
{{{b^2-4ac=-68}}}
Since the discriminant is negative, there are two imaginary, or complex roots, that solve the equation.
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b2) The full quadratic formula is 
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
{{{x = (4 +- sqrt(-68))/(2*3) }}} 
The exact solution is,
{{{x = (4 +- sqrt(68)i)/(6) }}}
The approximation is,  
{{{x = 0.67 +- 1.37i }}}