Find the discriminant of the following quadratic equation and hence determine the nature of the roots of the equation: $x^{2}-2x-15=0$.
(D) The given quadratic equation is $x^{2}-2x-15=0$.
Comparing this with the standard form $ax^{2}+bx+c=0$,we get $a=1$,$b=-2$,and $c=-15$.
The discriminant $D$ is given by the formula $D = b^{2}-4ac$.
Substituting the values: $D = (-2)^{2} - 4(1)(-15) = 4 + 60 = 64$.
Since $D > 0$ and $D$ is a perfect square $(8^{2} = 64)$,the roots of the equation are real,rational,and distinct.
Comparing this with the standard form $ax^{2}+bx+c=0$,we get $a=1$,$b=-2$,and $c=-15$.
The discriminant $D$ is given by the formula $D = b^{2}-4ac$.
Substituting the values: $D = (-2)^{2} - 4(1)(-15) = 4 + 60 = 64$.
Since $D > 0$ and $D$ is a perfect square $(8^{2} = 64)$,the roots of the equation are real,rational,and distinct.
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