Asked by Anonymous
Find two quadratic equations having the given solutions. (There are many correct answers. Use x for the variable. Enter your answers as a comma-separated list of equations.)
4+5√(5), 4-5√(5)
4+5√(5), 4-5√(5)
Answers
Answered by
Reiny
Using the sum and product properties of roots,
sum of roots = 4+5√(5) + 4-5√(5) = 8
product of roots = (4+5√5)(4-5√5)
= 16 - 25(5) = -109
so the simplest possible quadratic is
x^2 - 8x - 109 = 0
check: https://www.wolframalpha.com/input/?i=solve+x%5E2+-+8x+-+109+%3D+0
sum of roots = 4+5√(5) + 4-5√(5) = 8
product of roots = (4+5√5)(4-5√5)
= 16 - 25(5) = -109
so the simplest possible quadratic is
x^2 - 8x - 109 = 0
check: https://www.wolframalpha.com/input/?i=solve+x%5E2+-+8x+-+109+%3D+0
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