How do you find the value of the discriminant and determine the nature of the roots $2p^2+5p-4$ ?

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How do you find the value of the discriminant and determine the nature of the roots $2p^2+5p-4$ ?

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Answer 1 · 2017-06-06T05:15:20

$Delta = 57 > 0$ is not a perfect square, so the zeros are distinct, real and irrational.

Explanation:

Given:

$2p^2+5p-4$

Note that this is written in standard form:

$ap^2+bp+c$

with $a=2$ , $b=5$ and $c=-4$

The discriminant $Delta$ is given by the formula:

$Delta = b^2-4ac$

$color(white)(Delta) = color(blue)(5)^2-4(color(blue)(2))(color(blue)(-4))$

$color(white)(Delta) = 25+32$

$color(white)(Delta) = 57$

Since $Delta > 0$ the given quadratic has two distinct real zeros. Since $Delta = 57$ is not a perfect square, those zeros are irrational.

The zeros of $2p^2+5p-4$ are the roots of the equation:

$2p^2+5p-4 = 0$

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How do you find the value of the discriminant and determine the nature of the roots $2p^2+5p-4$ ?

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Explanation:

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How do you find the value of the discriminant and determine the nature of the roots $2p^2+5p-4$ ?