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1. Find the largest integer \(k\) such that the equation \(5x^2 - kx + 8 = 0\) has no real solutions.

2. What values of \(j\) does the equation \((2x+7)(x-5) = -43 + jx\) have one real solution?

 Jun 24, 2020
 #1
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Both of these involve using the discriminant \(b^2-4ac\).

 

1. Since there are no real solutions, \(b^2-4ac < 0\)

\((-k)^2-4*8*5 < 0\)

\(k^2 < 160\)

The largest integer k is 12.

 

2. First expand: \(2x^2-3x-35=-43+jx\)

Then combine like terms: \(2x^2-(3+j)x+8=0\)

Since there is one real solution, \(b^2-4ac = 0\)

\((-(3+j))^2-4*2*8=0\)

\(j^2+6j-55=0\)

\((j+11)(j-5)=0\)

So \(j=-11, 5\)

 Jun 24, 2020
 #2
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THXTHXTHXTHX!!!!!

 Jun 24, 2020

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