Question

What are the exact solutions of the quadratic equation x² – 5x - 1 = 0 using x = 2a?

a) 5+29/2
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b) 5−29/2
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c) 5+39/2
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d) 5−39/2
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Answer 1

The exact solutions of the quadratic equation x² – 5x - 1 = 0 are (5 ± √29) / 2.

Step-by-step explanation:

The quadratic equation x² – 5x - 1 = 0 can be solved using the quadratic formula. For an equation of the form ax² + bx + c = 0, the quadratic formula is:

x = (-b ± √(b² - 4ac)) / (2a)

Substituting the given values, we have:

x = (5 ± √((-5)² - 4(1)(-1))) / (2(1))

Calculating the expression inside the square root:

√(25 + 4) = √29

Therefore, the exact solutions of the quadratic equation are:

x = (5 ± √29) / 2