What is the nature of the roots of this equation:

${ 2x }^{ 2 }-5x=3$

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Check out the set:
2016 Problems
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Not Real
Real and Equal
Real and Distinct

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The nature of the roots can be found out by finding the discriminant which can in turn be found by applying the formula:- $b^2 - 4ac$

The equation can be written as $2x^2 -5x-3=0$

Here, $a = 2 ; b = -5 ; c = -3$

$D = {(-5)}^2 - (4×2×-3)$

$D = 25- (-24)$

$D = 25+24$

$D = 49$ which is greater than zero and a perfect square.

So, the roots of the equation are real, rational and distinct.