SOLUTION: Find k such that the equation 2x^2 +kx + 8 = 0 has two equal real roots, two distinct real roots and no real roots

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Question 1085175: Find k such that the equation 2x^2 +kx + 8 = 0 has two equal real roots, two distinct real roots and no real roots
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

2x%5E2+%2Bkx+%2B+8+=+0+->a=2, b=k, and+c=8
if the discriminant b%5E2-4ac%3E0, the equation has two distinct real roots
k%5E2-4%2A2%2A8%3E0
k%5E2-64%3E0
k%5E2%3E64
k%3Esqrt%2864%29
k%3E8

so, we can try k=9 which is greater than 8
2x%5E2+%2B9x+%2B+8+=+0
+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+2x%5E2+%2B9x+%2B+8+%29+




if the discriminant+b%5E2-4ac=0, the equation has two equal real roots
k%5E2-4%2A2%2A8=0
k%5E2-64=0
k%5E2=64
k=sqrt%2864%29
k=8
+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C++2x%5E2+%2B8x+%2B+8%29+

if the discriminant b%5E2-4ac%3C0, there are no real solutions
k%5E2-4%2A2%2A8%3C0
k%5E2-64%3C0
k%5E2%3C64
k%3Csqrt%2864%29
k%3C8


if k=7->
+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C++2x%5E2+%2B7x+%2B+8%29+

Answer by MathTherapy(10549) About Me  (Show Source):
You can put this solution on YOUR website!

Find k such that the equation 2x^2 +kx + 8 = 0 has two equal real roots, two distinct real roots and no real roots