Find the discriminant of the following quadratic equation and hence determine the nature of the roots of the equation: $x(x - 5) = 36$.
(D) The given equation is $x(x - 5) = 36$.
Expanding the equation: $x^2 - 5x = 36$.
Rearranging into the standard form $ax^2 + bx + c = 0$: $x^2 - 5x - 36 = 0$.
Here,$a = 1$,$b = -5$,and $c = -36$.
The discriminant $D$ is given by the formula $D = b^2 - 4ac$.
Substituting the values: $D = (-5)^2 - 4(1)(-36)$.
$D = 25 + 144 = 169$.
Since $D > 0$ and $169$ is a perfect square,the roots are real,rational,and distinct.
Expanding the equation: $x^2 - 5x = 36$.
Rearranging into the standard form $ax^2 + bx + c = 0$: $x^2 - 5x - 36 = 0$.
Here,$a = 1$,$b = -5$,and $c = -36$.
The discriminant $D$ is given by the formula $D = b^2 - 4ac$.
Substituting the values: $D = (-5)^2 - 4(1)(-36)$.
$D = 25 + 144 = 169$.
Since $D > 0$ and $169$ is a perfect square,the roots are real,rational,and distinct.
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