Let a and b be the roots of the quadratic x^{2 }- 5x + 3 = 0. Find the quadratic whose roots are a^{2 }and b^{2}.

x^{2 }+ filloutx + fillout

Fillout will equal the values of a and b squared

ZBRS7311 Jun 26, 2023

#1**-1 **

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

Guest Jun 26, 2023

#2**-1 **

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

Guest Jun 26, 2023