Question

Always True, Sometimes True, or Never True? Please help! (will MEDAL AND FAN)

Answer 1

@ganeshie8 Would you help please?

Answer 2

@campbell_st quick help?

Answer 3

ok... so for the 1st question can you have an equation such as

\[y = x^2 + 4\]

will it have real solutions... given it has real coefficients?

Answer 4

this also helps with the 2nd question as this polynomial doesn't cut the x- axis... its a positive definite parabola

Answer 5

given we can't give answers, the example above should head you in the right direction.

Answer 6

@campbell_st when I graphed the first equation you gave me it doesn't touch the X axis at all..

Answer 7

so it has real coefficients and no real roots.... so which choice do you think is best..?

Answer 8

Sometimes true for the first one correct?

Answer 9

i would agree

Answer 10

Okay Lets go onto the second one?

Answer 11

what do you think based on the response of @campbell_st

Answer 12

so the 2nd question you graphed

\[y = x^2 + 4\]

did it cut the x-axis... does it have real or complex roots..?

Answer 13

didn't cut the X axis @campbell_st

Answer 14

so are the solutions complex or real..?

Answer 15

set y = 0 and solve

\[x^2 + 4 = 0\]

will the answer be real numbers or complex numbers...

Answer 16

Real numbers

Answer 17

wait, complex numbers sorry

Answer 18

well

\[x^2 = -4\]

so

\[x = \sqrt{-4}\]

you need to identify that you can't take the square root of a negative number

you need the complex identity

\[i^2 = -1\]

so the problem is now \[x = \sqrt{4i^2} = \pm 2i\]

so any thoughts on the correct answer

Answer 19

complex is correct so the 1st choice looks good

Answer 20

the last one... I'd choose the 1st option...

Answer 21

Okay I see what you did thanks a lot!