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(D) The given equation is $2x^{2} - 3x - 5 = 0$.Comparing this with the standard form $ax^{2} + bx + c = 0$,we get:$a = 2, b = -3, c = -5$.The quadrat

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$\frac{5}{2}, -1$

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(D) The given equation is $2x^{2} - 3x - 5 = 0$.Comparing this with the standard form $ax^{2} + bx + c = 0$,we get:$a = 2, b = -3, c = -5$.The quadratic formula is given by $x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}$.Substituting the values:$x = \frac{-(-3) \pm \sqrt{(-3)^{2} - 4(2)(-5)}}{2(2)}$$x = \frac{3 \pm \sqrt{9 + 40}}{4}$$x = \frac{3 \pm \sqrt{49}}{4}$$x = \frac{3 \pm 7}{4}$.Calculating the two roots:$x_{1} = \frac{3 + 7}{4} = \frac{10}{4} = \frac{5}{2}$$x_{2} = \frac{3 - 7}{4} = \frac{-4}{4} = -1$.Thus,the roots of the equation are $\frac{5}{2}$ and $-1$.

Find the roots of the quadratic equation using the quadratic formula:
$2x^{2} - 3x - 5 = 0$

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Find the roots of the quadratic equation using the quadratic formula:$2x^{2} - 3x - 5 = 0$