If x² – 3x + 2 is one of the zeros of x⁴ – px² + q then the values of p and q are

Factorise x² – 3x + 2 = (x – 1)(x – 2). So x = 1 and x = 2 are roots of x⁴ – px² + q.

Put in x = 1: 1 – p + q = 0. Put in x = 2: 16 – 4p + q = 0.

Subtract the first from the second: 15 – 3p = 0, so p = 5. Then q = p – 1 = 4. So p = 5 and q = 4.