SOLUTION: The roots of the equation 4x^2-x+36=0 are (alpha)^2 and (beta)^2. Find: (a) an equation whose roots are 1/(alpha)^2 and 1/(beta)^2 , (b) two distinct equations whose roots are (

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: The roots of the equation 4x^2-x+36=0 are (alpha)^2 and (beta)^2. Find: (a) an equation whose roots are 1/(alpha)^2 and 1/(beta)^2 , (b) two distinct equations whose roots are (      Log On


   

Question 173794: The roots of the equation 4x^2-x+36=0 are (alpha)^2 and (beta)^2. Find:
(a) an equation whose roots are 1/(alpha)^2 and 1/(beta)^2 ,
(b) two distinct equations whose roots are (alpha) and (beta).
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
4x%5E2+-+x+%2B+36+=+0
Use quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+4
b+=+-1
c+=+36
x+=+%28-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2-4%2A4%2A36+%29%29%2F%282%2A4%29
x+=+%28+1+%2B-+sqrt%28+1+-+576+%29%29+%2F+8+
x+=+%28+1+%2B-+5%2Asqrt%28+-23+%29%29+%2F+8+
x+=+%28+1+%2B-+5%2Asqrt%2823%29%2Ai%29+%2F+8+
a%5E2+=+%281+%2B+5%2Asqrt%2823%29%2Ai%29%2F8
b%5E2+=+%281+-+5%2Asqrt%2823%29%2Ai%29%2F8
1%2Fa%5E2+=+8%2F%281+%2B+5%2Asqrt%2823%29%2Ai%29
1%2Fb%5E2+=+8%2F%281+-+5%2Asqrt%2823%29%2Ai%29
If roots are r%5B1%5D and r%5B2%5D,


r%5B1%5D+%2B+r%5B2%5D+=+8%2A%281+-+5%2Asqrt%2823%29%2Ai+%2B+1+%2B+5%2Asqrt%2823%29%2Ai%29
r%5B1%5D+%2B+r%5B2%5D+=+16

r%5B1%5Dr%5B2%5D+=+64+%2F+%281+-+25%2A23%2A%28-1%29%29
r%5B1%5Dr%5B2%5D+=+64+%2F+576
r%5B1%5Dr%5B2%5D+=+1%2F9
The equation is

%28x+-+r%5B1%5D%29%28x+-+r%5B2%5D%29+=+x%5E2+-+16x+%2B++%281%2F9%29
x%5E2+-+16x+%2B+%281%2F9%29+=+0
9x%5E2+-+144x+%2B+1+=+0 answer
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I'm not sure what the next part is looking for