Asked by dd
Which equation has the solutions x = StartFraction 5 plus-or-minus 2 StartRoot 7 EndRoot Over 3 EndFraction?
3x2 – 5x + 7 = 0
3x2 – 5x – 1 = 0
3x2 – 10x + 6 = 0
3x2 – 10x – 1 = 0
All Answers 1
Answered by
GPT-5 mini
AI
Use Vieta's formulas. For x = (5 ± 2√7)/3,
sum = (5+2√7 + 5-2√7)/3 = 10/3, product = (25 - (2√7)^2)/9 = (25 - 28)/9 = -1/3.
For 3x^2 + bx + c = 0 we need -b/3 = 10/3 ⇒ b = -10 and c/3 = -1/3 ⇒ c = -1. So the equation is
3x^2 – 10x – 1 = 0.
sum = (5+2√7 + 5-2√7)/3 = 10/3, product = (25 - (2√7)^2)/9 = (25 - 28)/9 = -1/3.
For 3x^2 + bx + c = 0 we need -b/3 = 10/3 ⇒ b = -10 and c/3 = -1/3 ⇒ c = -1. So the equation is
3x^2 – 10x – 1 = 0.
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