SOLUTION: the roots of 2x^2 +3x-1=0 are alpha and beta. Find the values of alpha square -beta square

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Question 1187914: the roots of 2x^2 +3x-1=0 are alpha and beta. Find the values of alpha square -beta square


Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
2x%5E2+%2B3x-1=0+ are alpha+and beta
find roots using quadratic formula
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29+......a=2,b=3%2C+and+%7B%7B%7Bc=-1
x=%28-3%2B-sqrt%283%5E2-4%2A2%28-1%29%29%29%2F%282%2A2%29+
x=%28-3%2B-sqrt%289%2B8%29%29%2F4+
x=%28-3%2B-sqrt%2817%29%29%2F4+

=> alpha+=%28-3%2Bsqrt%2817%29%29%2F4+ and beta=%28-3-sqrt%2817%29%29%2F4+

Find the values of alpha%5E2+-beta%5E2:



alpha%5E2+-beta%5E2=%28-3%2Bsqrt%2817%29%29%5E2%2F16+-%28-3-sqrt%2817%29%29%5E2%2F16

alpha%5E2+-beta%5E2=%2826+-+6+sqrt%2817%29%29%2F16+-%2826+%2B+6+sqrt%2817%29%29%2F16

alpha%5E2+-beta%5E2=%2826+-+6+sqrt%2817%29+-26+-+6+sqrt%2817%29%29%2F16

alpha%5E2+-beta%5E2=%28+-+12+sqrt%2817%29%29%2F16

alpha%5E2+-beta%5E2=-%283sqrt%2817%29%29%2F4