What is the positive solution to the equation 0 = –x2 + 2x + 1? Quadratic formula: x = StartFraction negative b plus or minus St
artRoot b squared minus 4 a c EndRoot Over 2 a EndFraction
1 answer:
Answer:
x = 2 + √2
x = 2 - √2
Step-by-step explanation:
- x² + 2x + 1 = 0
x² - 2x - 1 = 0
Here,
a = <em>1</em>
b = <em>- 2</em>
c = <em>- 1</em>
Now,
Discriminant
D = b² - 4ac
= (-2)² - 4(1)(-1)
= 4 + 4
= 8
=2√2 > 0
<em><u>Real and </u></em><em><u>D</u></em><em><u>istinct roots </u></em>
x = - b +- √b² - 4ac/2a
= - (-2) +- √ = (-2)² - 4(1)(-1)/2(1)
= 2 +- √4 + 4/2
= 2 +- √8/2
= 2 +- 2√2/2
= 2 +- √2
x = 2 + √2 or x = 2 - √2
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