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Let a and b be the roots of the quadratic x- 5x + 3 = 0. Find the quadratic whose roots are aand b2.

 

x+ filloutx + fillout

 

Fillout will equal the values of a and b squared 

 Jun 26, 2023
 #1
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The quadratic whose roots are a2 and b2 is given by:

x2 - (a2 + b2)x + ab2 = 0

We can find the value of a2 + b2 using the following formula:

a2 + b2 = (a + b)2 - 2ab

In this case, a + b = 5 and ab = 3. Therefore, a2 + b2 = 52 - 2*3 = 23.

We can find the value of ab2 using the following formula:

ab2 = a2b2 = (ab)2 = 32 = 9

Therefore, the quadratic whose roots are a^2 and b^2 is given by:

x2 - 23x + 9 = 0

 Jun 26, 2023
 #2
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The quadratic whose roots are a2 and b2 is given by:

x2 - (a2 + b2)x + ab2 = 0

We can find the value of a2 + b2 using the following formula:

a2 + b2 = (a + b)2 - 2ab

In this case, a + b = 5 and ab = 3, so a2 + b2 = 29.

We can find the value of ab2 using the following formula:

ab2 = a2b2 = (ab)(a2) = 3 * 29 = 87

Therefore, the quadratic whose roots are a2 and b2 is given by:

x2 - 29x + 87 = 0

 Jun 26, 2023
 #3
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Spread the misinformation and s***w over the homework cheaters!

Guest Jun 27, 2023
 #4
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The sum of the roots of the quadratic x2 - 5x + 3 = 0 is 5, and the product of the roots is 3. Therefore, the quadratic whose roots are a2 and b2 is

x2 - (a2 + b2)x + (a2)(b2) = x2 - 5x + 9

The answer is x2 - 5x + 9.

 Jun 27, 2023
 #5
avatar+84 
+1

This question's hint was to use the Vieta's Formula reverse

 Jun 29, 2023

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