SOLUTION: Hi. Please help. I am lost-my mind is swimming with all the steps and I got lost twice-I need HELP! The problem is: State the value of the discriminant and the number of real sol

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Hi. Please help. I am lost-my mind is swimming with all the steps and I got lost twice-I need HELP! The problem is: State the value of the discriminant and the number of real sol      Log On


   

Question 133011: Hi.
Please help. I am lost-my mind is swimming with all the steps and I got lost twice-I need HELP!
The problem is: State the value of the discriminant and the number of real solutions. t^2+14t+49=0
Thank You.
Found 2 solutions by jim_thompson5910, solver91311:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
From the quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

the discriminant consists of all of the terms in the square root. So the discriminant is

D=b%5E2-4ac

the discriminant tells us how many solutions (and what type of solutions) we can expect for any quadratic.


Now let's find the discriminant for y=t%5E2%2B14t%2B49:

D=b%5E2-4ac Start with the given equation

D=%2814%29%5E2-4%2A1%2A49 Plug in a=1, b=14, c=49

D=196-4%2A1%2A49 Square 14 to get 196

D=196-196 Multiply -4*1*49 to get -196

D=0 Combine 196 and -196 to get 0


Since the discriminant equals 0 , this means there is one real solution. Remember if the discriminant is equal to zero, then the quadratic will have one real solution.



Notice if we graph y=t%5E2%2B14t%2B49, we can see that there is one real solution. So this verifies our answer.

+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2%2B14x%2B49%29+

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ is the quadratic formula. The discriminant is the part under the radical, or b%5E2-4%2Aa%2Ac

Your equation, t%5E2%2B14t%2B49=0 is already in standard ax%5E2%2Bbx%2Bc=0 form, so just plug in the numbers:

14%5E2-4%2A1%2A49=196-196=0 is the value of the discriminant.

A discriminant of 0 means that there are two real and identical roots (or 1 real root with a multiplicity of 2, depending on the terminology you have been taught)