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Let a and b be the solutions to 5x^2 - 11x + 4 = 0. Find 1/a + 1/b

 Jun 28, 2020
 #1
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The roots are (15 +/- sqrt(145))/10, and 1/a + 1/b = 7/5.

 Jun 28, 2020
 #2
avatar+146 
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Let a and b be the solutions to \(5x^2-11x+4=0\). Find \(1/a + 1/b\) .

 

According to Vieta's Formula, the sum of the two roots are \(-b/a \) and the product of the roots is \(c/a\) for an equation in the form of\(ax^2+bx+c=0\) .

In this case, \(a=5, b= -11,\) and \(c=4\) .

We can factor \(1/a + 1/b\) to become \((a+b)/ab\). We can plug our values for a, b, and c in for the sum and product of the roots, giving us the answer of \(11/4\) . We don't need to solve for the roots.

Therefore our answer is 11/4

I hope this helped.

 Jun 28, 2020
 #3
avatar+102 
0

Use Vieta's formulas.

 

sum of roots = -b/a

product of roots = c/a

 

then do some manipulation, don't be lazy

 Jun 28, 2020

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