1if the discriminnt of a quadratic equation is 48 then deter

1.if the discriminnt of a quadratic equation is 48, then determine the number and type of solutions of the equation.

2.use the discriminant to determine the number and type of solutions of the equations: 5-4x+12x^2=0

3.simplify: square root of 5y^11 over square root of 2y

4.simplify: (square root of 80y^6) - square root of 20y^6

5. rationalize the denominator: 1 over (suare root 5) + 3

6. Simplify and write your answer in i notation: square root -44

7. Simplify and write your answer in a+bi notation: (15 + 2i) – (18 – 5i)

8.Simplify and write your answer in a+bi notation: 6i(3 – 8i)

9.Find the distance between the points (-3, 5) and (2, 8).

1. if the discriminnt of a quadratic equation is >0 , so there would be two real roots.

2. 5 - 4x+12x^2=0

discrimnant : b^2 -4ac = (-4)^2 - 4*5*12

= 16 - 240

= -224

if the discriminnt of a quadratic equation is <0 , so there would be two complex roots.

3. sqrt(5y^11)/sqrt(2y)

= 5^1/2*y^11/2 / 2^1/2*y^1/2

= 5^1/2y/2^1/2*y^1/2

=(5/2)^1/2*y^(11/2 -1/2)

=(5/2)^1/2*y^5

4 sqrt(80y^6) - sqrt(20y^6)

= y^3[ sqrt80 - sqrt20 ]

= y^3[2sqrt20 - sqrt20]

= y^3[sqrt20]

= y^3*2sqrt5

= 2y^3sqrt(5)