SOLUTION: Find the largest value of k such that the roots of the equation 2x^2+5x+k=0 are real.

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Question 369498: Find the largest value of k such that the roots of the equation 2x^2+5x+k=0 are real.
Found 2 solutions by Fombitz, CharlesG2:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use the discriminant,
D=b%5E2-4ac
D=5%5E2-4%282%29k
If D%3C0, the roots become complex.
Solve for D=0
25-8k=0
8k=25
highlight%28k=25%2F8%29


Answer by CharlesG2(834) About Me  (Show Source):
You can put this solution on YOUR website!
Find the largest value of k such that the roots of the equation 2x^2+5x+k=0 are real.

2x^2 + 5x + k = 0
this is of form ax^2 + bx + c = 0,
which is a quadratic equation,
a = 2, b = 5, c = k
use the discriminant b^2 - 4ac from the quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
b^2 - 4ac = 5^2 - 4(2)k = 25 - 8k
the disciminant needs to be greater than or equal to 0 for there
to be real roots
25 - 8k >= 0
-8k >= -25
8k <= 25 (flipped sign since divided by negative)
k <= 25/8
k <= 3 1/8
k <= 3.125
the largest k such that the roots are real is 25/8 or 3.125