How do you find the discriminant and how many solutions does $9u^2-24u+16$ have?

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Answer 1 · 2015-05-13T06:49:24

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

$a=9, b=-24, c=16$

The Discriminant is given by:

$Delta=b^2-4*a*c$

$= (-24)^2-(4*(9)*16)$

$= 576-576=0$

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 $Delta = 0$ , this equation has ONE REAL SOLUTION

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

As $Delta = 0$ , $u = (-(-24)+-sqrt(0))/(2*9) = 24/18 = 4/3$

How do you find the discriminant and how many solutions does 9u^2-24u+169u^2-24u+16 have?