fine the value of the discriminant and discribe the nature of the roots of each quadriatic equation?

Question

9u2-24u+16=0

Answer 1

9u^2-24u+16=0
discriminant
=(-24)^2-4*9*16
=0
since it is = 0
so its roots are real and
equal

Answer 2

By the quadratic formula, the discriminant is b^2-4ac. So this discriminant is exactly 0! This means that both roots are the same, and that this quadratic is a perfect square. This is because in the "plus or minus" part of the quadratic formula, "+0" = "-0". Hope this helps!

Answer 3

using the quadratic formula the discriminant is the part under square root on equation of for au2+bu+c
so a=9 b=-24 and c=16

find b2-4ac or (-24)2 - 4*9*16
or 576 - 576 = 0. disid criminant = 0, one root
if discriminant is negative, no real roots
zero on real root
positive, two real roots

Answer 4

Discriminant = b^2 - 4ac
=24^2 -4*9*16
=0

Zero discriminant means roots are equal. You have information in notes or textbook about what else the discriminant tells us about the roots? whether the discriminant is + or -, perfect square or not?

Answer 5

discriminant=b2-4ac
here b= -24
hence, b2= (-24)2= 576
a=9
c=16
hence, 4ac= 4x9x16=576
now, b2-4ac= 576-576= 0
since the value of the discriminant(d)=0, both the roots are equal.
note:
when
d<0, the roots are not real.
d>0, the roots are real.
d=0,the roots are equal.

Answer 6

a = 9
b = -24
c = 16
b^2- 4ac = (-24)^2 - 4*9* 16 = 0

so discriminant = 0

so it has a double root -4/3

equation is (3u-4)^2 = 0

Answer 7

9u2-24u+16=0
discriminent=b^2-4ac=(-24)^2-4*9*16=576-576=0
so this is a perfect square.
(3u-4)^2=0
u=4/3

Answer 8

if ax^2 + bx + c = 0
then the discriminant is b^2 - 4ac.
If the discriminant is less than zero, there are no real roots,
only complex roots.

If it equals zero , there is one real root.

If it is greater than zero, there are two real roots.