Solve the quadratic equation below by the quadratic formula. Write the EXACT answers in simplified form. x^2 −5x+7=0

Question

asked Feb 21, 2024 26.7k views

1 Answer

Sagar Ranpise · Answer 1 · 2024-02-25T05:59:45+0000

Answer:

$x=(5\pm i√(3))/(2)$

Explanation:

You want to solve the quadratic equation x² −5x +7 = 0 using the quadratic formula.

The coefficients in the given equation are a = 1, b = -5, c = 7. The quadratic formula is ...

$x=(-b\pm√(b^2-4ac))/(2a)$

Using the coefficients for the given equation, the solutions are ...

$x=(-(-5)\pm√((-5)^2-4(1)(7)))/(2(1))=(5\pm√(-3))/(2)\\\\\\\boxed{x=(5\pm i√(3))/(2)}$

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Additional comment

The square root of a negative number is imaginary.

√(-3)=(√(-1))(√(3))=i√(3)

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