How do you find the discriminant and how many solutions does $-7d^2 + 2d + 9 = 0$ have?

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Answer 1 · 2015-05-11T11:51:42

The equation is of the form $color(blue)(ax^2+bx+c=0$ where:

$a=-7, b=2, c=9$

The Disciminant is given by :
$Delta=b^2-4*a*c$
$= (2)^2-(4*(-7)*9)$
$= 4-(-252)=4+252=256$

If $Delta=0$ then there is only one solution.
(for $Delta>0$ there are two solutions,
for $Delta<0$ there are no real solutions)

As $Delta = 256$ , this equation has TWO REAL SOLUTIONS

Note :
The solutions are normally found using the formula
$x=(-b+-sqrtDelta)/(2*a)$

As $Delta = 256$ , $x = (-(2)+-sqrt256)/(2*-7) = (-2+-16)/(-14) = 14/-14 or (-18)/-14 = -1 or 9/7$

$color(green)(x = -1,9/7$ are the two solutions

How do you find the discriminant and how many solutions does -7d^2 + 2d + 9 = 0-7d^2 + 2d + 9 = 0 have?