Answer:
The values of p and q such that 2·x² - 4·x + 3 = 2·(x - p)² + q, are;
p = 1, q = 1
Step-by-step explanation:
The given equation are;
2·x² - 4·x + 3 = 2·(x - p)² + q
By expanding the right hand side of the equation, we have;
2·x² - 4·x + 3 = 2·(x - p)² + q = 2·x² - 4·p·x + 2·p² + q
2·x² - 4·x + 3 = 2·x² - 4·p·x + 2·p² + q
Comparing the coefficient of x in both equations, gives;
2·x² + (- 4)·x + 3 = 2·x² + (- 4·p)·x + 2·p² + q
-4 = -4·p
∴ p = -4/(-4) = 1
p = 1
Comparing only the constant terms (terms not multiplied by "x" or "x²"), we get;
3 = 2·p² + q
Substituting the value for "p" obtained above (p = 1 ) in the previous equation, we get;
3 = 2 × 1² + q = 2 + q
∴ q = 3 - 2 = 1
q = 1.
