Final answer:
To find the values of p and q, the quadratic equation must be transformed into a perfect square trinomial by completing the square. After factoring and manipulating the equation, it is determined that p = 1 and q = 1.
Step-by-step explanation:
To find the values of p and q in the equation given by the student, we need to rewrite the quadratic equation 2x² - 4x + 3 in the form of 2(x - p)² + q. We do this by completing the square, a method used to transform a quadratic equation into a perfect square trinomial.
First, we factor out the coefficient of the x² term which is 2:
/2(x² - 2x) + 3
To complete the square, we take half of the coefficient of x, square it, and add it inside the parentheses:
/(x - 1)², since (2/2)² = 1.
We must also subtract the same value outside the parentheses to keep the equation balanced. This value is subtracted times the coefficient from the beginning, 2:
/(x - 1)² - 2(1) + 3 = 2(x - 1)² + 1
Comparing this to the form 2(x - p)² + q, we conclude that p is 1, since x is subtracted by 1, and q is 1, the constant term outside the parentheses.
Thus, the values are p = 1 and q = 1.