Determine the nature of the roots: 4x^2 + 32x + 64 = 0 a. no real solutions b. a unique real solution c. two distinct real solutions d. cannot be determined

b. a unique real solution

Step-by-step explanation:

A quadratic equation ax² + bx + c = 0 ,

Has two distinct real roots,

If discriminant,

Has two equal real roots,

If D = 0,

Has two imaginary roots or no real roots,

if D < 1,

Here. the given qudratic equation,

By comparing,

a = 4, b = 32, c = 64,

Hence, the equation has two equal real roots or a unique real solution.

i.e. OPTION 'b' is correct.

b

step-by-step explanation:

a difference is the result of subtraction. while each of these expressions has subtraction in it, a difference will be the result when subtraction is the last operation applied in the order of operations for the expression. this means subtraction must be outside of the parenthesis. only b has this.

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.