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Math Help - Calculate a and b ( goemetric sequance question)

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    Calculate a and b ( goemetric sequance question)

    Let x1 and x2 be the roots of the equation x^2-3x+a=0, x3 and x4 the roots of the equation x^2-12x+b=0
    Calculate the constants a and b so that x1 ,x2,x3 and x4 form an increasing goemetric sequance
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  2. #2
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    Re: Calculate a and b ( goemetric sequance question)

    Quote Originally Posted by lebanon View Post
    Let x1 and x2 be the roots of the equation x^2-3x+a=0, x3 and x4 the roots of the equation x^2-12x+b=0
    Calculate the constants a and b so that x1 ,x2,x3 and x4 form an increasing goemetric sequance
    From what we know about sums and products of roots of quadratics we have x1+x2=3 x1*x2=a x3+x4=12 and x3*x4=b
    Let r = the common ratio of the geometric sequence. Then x2=r*x1, x3=r^2*x1 and x4=r^3*x1
    **
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