+95
Let a and b be the roots of the quadratic x2 - 5x + 3 = 0. Find the quadratic whose roots are a2 and b2.
x2 + filloutx + fillout
Fillout will equal the values of a and b squared
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
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
