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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.

55 A If Alpha And Beta Are The Roots Of The Equation Xsquare Pxq0 And Betagtalpha Find The Square Of The Difference Of The Roots In Terms Of P And Q class=

Sagot :

Coolstickidn

Answer:

√(p²-4q)

Step-by-step explanation:

Using the Quadratic Formula, we can say that

x = ( -p ± √(p²-4(1)(q))) / 2(1)  with the 1 representing the coefficient of x². Simplifying, we get

x = ( -p ± √(p²-4q)) / 2

The roots of the function are therefore at

x = ( -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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