MATH SOLVE

9 months ago

Q:
# Find the value of q, for which the difference between the roots in the equation x2β10x+q=0 is equal to 6.

Accepted Solution

A:

According to the quadratic formula, -b plus or minus β(b^2 - 4ac)x = ---------------------------------------------- 2a

In this particular case (x^2 - 10x + q), a = 1, b = -10, and c = q. Thus: -(-10) plus or minus β(100-4q) 10 plus or minus β4β(25-q)x = ---------------------------------------------- = --------------------------------------------- 2 2

and this reduces to:x = 5 plus or minus β(25-q).Assuming that 5 + β(25-q) is larger than 5 - β(25-q), we can write:5 + β(25-q) - (5 - β(25-q)) = 6, or β(25-q) + β(25-q) = 6, or β(25-q) = 3.Squaring both sides, we get: 25-q = 9, orq = 16 (answer)If q = 16, then the difference between the two roots will be +6.

In this particular case (x^2 - 10x + q), a = 1, b = -10, and c = q. Thus: -(-10) plus or minus β(100-4q) 10 plus or minus β4β(25-q)x = ---------------------------------------------- = --------------------------------------------- 2 2

and this reduces to:x = 5 plus or minus β(25-q).Assuming that 5 + β(25-q) is larger than 5 - β(25-q), we can write:5 + β(25-q) - (5 - β(25-q)) = 6, or β(25-q) + β(25-q) = 6, or β(25-q) = 3.Squaring both sides, we get: 25-q = 9, orq = 16 (answer)If q = 16, then the difference between the two roots will be +6.