SOLUTION: Find the smallest integral value of c that will produce imaginary roots in the equation: 4x^2-7x+c=0

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Question 844058: Find the smallest integral value of c that will produce imaginary roots in the equation: 4x^2-7x+c=0
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Look at the discriminant, D=b%5E2-4ac
D=%28-7%29%5E2-4%284%29%28c%29
D=49-16c
For complex roots, the discriminant is negative.
49-16c%3C0
-16c%3C-49
c%3E49%2F16
48%2F16=3 so the next integer value is c=4
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graph%28300%2C300%2C-1%2C4%2C-1%2C4%2C4x%5E2-7x%2B3%2C4x%5E2-7x%2B4%29
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Shown are graphs of 4x%5E2-7x%2B3(Red) with real roots and 4x%5E2-7x%2B4(Green) with no real roots.