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$X^2 - 10X + 26 = 0$ with the solutions $X^2 = i$ and $-i$

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Write and solve direct variation equations

Full solution

Q.

X^2 - 10X + 26 = 0

with the solutions

X^2 = i

and

-i

Write Equation: Step $1$ : Write down the given quadratic equation. $\newline$ Equation: $x^2 - 10x + 26 = 0$
Use Quadratic Formula: Step $2$ : Use the quadratic formula to solve for $x$ . The formula is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ . Here, $a = 1$ , $b = -10$ , and $c = 26$ . Calculate the discriminant $b^2 - 4ac$ . Discriminant = $(-10)^2 - 4\cdot1\cdot26 = 100 - 104 = -4$
Calculate Solutions: Step $3$ : Since the discriminant is negative $(-4$ ), the solutions are complex numbers. $\newline$ Calculate the solutions using the quadratic formula. $\newline$ $x = \frac{-(-10) \pm \sqrt{-4}}{2\cdot1}$ $\newline$ $x = \frac{10 \pm 2i}{2}$ $\newline$ $x = 5 \pm i$

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