Examine the quadratic equation 9x^2+24x+16=0.
a: what is the discriminant of the quadratic equation?
b: based on the discriminant, which statement about the roots of the quadratic equation is correct?
select one answer choice for question a, and select one answer choice for question b.
a: 120
a: -120
a: 0
b: there is one real root with a multiplicity of 2.
b: there are two real roots.
b: there are two complex roots

The correct answer options are,

A: 0

B: There is one real root with a multiplicity of 2.

Step-by-step explanation:

Discriminant of a quadratic equation ax² + bx + c = 0 is given by,

b² - 4ac

It is given a quadratic equation 9x² + 24x + 16 = 0

To find the discriminant

Here a = 9, b = 24 and c = 16

Discriminant = b² - 4ac

 = 24² - (4 * 9 * 16)

 = 576 - 576

 = 0

The correct options are

A: 0

B: There is one real root with a multiplicity of 2.

hello from mrbilldoesmath!

answer:   (7x + 6y) ( 49x^2 - 42xy + 36y^2)

discussion:

in general, the factorization of a^3 + b^3 is

a^3 + b^ 3 = (a + b) ( a^2 - ab + b^2)

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

(7x + 6y) ( 49x^2 - 42xy + 36y^2)

you,

mrb

(a + b) (a^2 - a b + b^2)