55. (a) If alpha and beta are the roots of the equation xsquare+ px+q=0 and beta>alpha find the square of the difference of the roots in terms of p and q.

1 answer
Question:

55. (a) If alpha and beta are the roots of the equation xsquare+ px+q=0 and beta>alpha find the square of the
difference of the roots in terms of p and q.

Answers

Answer:√(p²-4q)Step-by-step explanation:Using the Quadratic Formula, we can say thatx = ( -p ± √(p²-4(1)(q))) / 2(1)  with the 1 representing the coefficient of x². Simplifying, we getx = ( -p ± √(p²-4q)) / 2The roots of the function are therefore atx = ( -p + √(p²-4q)) / 2 and x = ( -p - √(p²-4q)) / 2. The difference of the roots is thus( -p + √(p²-4q)) / 2 - ( ( -p - √(p²-4q)) / 2)= 0 + 2 √(p²-4q)/2= √(p²-4q)

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