How to use the discriminant to find out how many real number roots an equation has for $x^{2} - 5 x + 7 = 0$ $x^2 - 5x + 7 = 0$ ?

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Answer 1 · 2015-05-17T09:47:03

$x^{2} - 5 x + 7$ $x^2-5x+7$ is of the form $a x^{2} + b x + c$ $ax^2+bx+c$ , with $a = 1$ $a=1$ , $b = - 5$ $b=-5$ and $c = 7$ $c=7$ .

The discriminant is given by the formula:

$Delta = b^2-4ac$

$= (-5)^2-(4xx1xx7) = 25-28 = -3$

Being negative, we can deduce that $x^2-5x+7=0$ has no real roots (it has two distinct complex roots).

How to use the discriminant to find out how many real number roots an equation has for x^2 - 5x + 7 = 0x2−5x+7=0x^2 - 5x + 7 = 0?