The roots of the quadratic equation x + frac{ | vedclass

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Question

(A) Given equation: $x + \frac{2}{x} = 3$Multiply the entire equation by $x$ to eliminate the denominator:$x^2 + 2 = 3x$Rearrange the equation into th

Vedclass · Accepted Answer

$2$ and $1$

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(A) Given equation: $x + \frac{2}{x} = 3$Multiply the entire equation by $x$ to eliminate the denominator:$x^2 + 2 = 3x$Rearrange the equation into the standard form $ax^2 + bx + c = 0$:$x^2 - 3x + 2 = 0$Factor the quadratic equation:$x^2 - 2x - x + 2 = 0$$x(x - 2) - 1(x - 2) = 0$$(x - 2)(x - 1) = 0$Setting each factor to zero:$x - 2 = 0 \implies x = 2$$x - 1 = 0 \implies x = 1$Thus,the roots are $2$ and $1$.

The roots of the quadratic equation $x + \frac{2}{x} = 3$ are $\dots$ $(x \neq 0)$.

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