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Form the quadratic whose roots are the squares of the roots of $x^{2} - 3 x + 2 = 0$ .

Competition practiceAlgebra

A $x^{2} - 5 x + 4 = 0$
B $x^{2} - 9 x + 4 = 0$
C $x^{2} - 5 x + 2 = 0$
D $x^{2} + 5 x + 4 = 0$

Step-by-Step Solution

The roots are 1 and 2, so the new roots are 1 and 4: sum 5, product 4, giving

x^{2} - 5 x + 4 = 0

.

Answer: A)

x^{2} - 5 x + 4 = 0

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