Find the discriminant of the following quadratic equation and hence determine the nature of the roots of the equation: $4x^{2}-6x+2=0$.
(A) For the quadratic equation $ax^{2}+bx+c=0$,the discriminant $D$ is given by $D = b^{2}-4ac$.
Comparing $4x^{2}-6x+2=0$ with the standard form,we get $a=4$,$b=-6$,and $c=2$.
Substituting these values into the formula: $D = (-6)^{2} - 4(4)(2) = 36 - 32 = 4$.
Since $D > 0$ and $D$ is a perfect square,the roots are real,rational,and distinct.
Comparing $4x^{2}-6x+2=0$ with the standard form,we get $a=4$,$b=-6$,and $c=2$.
Substituting these values into the formula: $D = (-6)^{2} - 4(4)(2) = 36 - 32 = 4$.
Since $D > 0$ and $D$ is a perfect square,the roots are real,rational,and distinct.
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