Nature of roots of quadratic equations

by thornluke
 P: 37 1. The problem statement, all variables and given/known data The equation kx2 - 3x + (k+2) = 0 has two distinct real roots. Find the set of possible values of k. 2. Relevant equations Since the equation has two distinct real roots, b2 - 4ac > 0 3. The attempt at a solution b2-4ac>0 9-4(k+2)(k)>0 9-4(k2+2k) >0 9-4k2-8k>0 = -4k2-8k+9>0 Multiply both sides by -1, 4k2+8k-9>0 (4k-3)(k+3)>0 -3
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P: 7,076
 Quote by thornluke 1. The problem statement, all variables and given/known data The equation kx2 - 3x + (k+2) = 0 has two distinct real roots. Find the set of possible values of k. 2. Relevant equations Since the equation has two distinct real roots, b2 - 4ac > 0 3. The attempt at a solution b2-4ac>0 9-4(k+2)(k)>0 9-4(k2+2k) >0 9-4k2-8k>0 = -4k2-8k+9>0 Multiply both sides by -1, 4k2+8k-9>0 (4k-3)(k+3)>0 -3

(4k-3)(k+3) = 4k2 + 9k - 9 .

Also, multiplying by -1 will change > to < .

Solve 4k2+8k-9 = 0 by using the quadratic formula --- or by completing the square.
P: 37
 Quote by SammyS Your factoring is incorrect. (4k-3)(k+3) = 4k2 + 9k - 9 . Also, multiplying by -1 will change > to < . Solve 4k2+8k-9 = 0 by using the quadratic formula --- or by completing the square.
((-8 ± √208)/8) < 0

-2.80 < k < 0.80

I'm getting closer to the "answer" (-2.46<k<0.458) am I wrong, or is the "answer" wrong?

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P: 1,338

Nature of roots of quadratic equations

I'm getting the same roots (-2.80 and 0.80).

When I played around with the coefficients of the original quadratic, I found that if you made the coefficient of the x2 term 2k:
2kx2 - 3x + (k+2) = 0
You will get the original answer that you stated: -2.4577 < k < 0.4577. So it looks like either you copied the problem incorrectly or the book has a typo somewhere.
 PF Patron HW Helper Sci Advisor Emeritus P: 7,076 The text book's answer is consistent with -8k2 - 16k +9 > 0 . equivalent to -4k2 - 8k + 9/2 >0 It's hard to see how that's from a simple Typo -- unless the coefficient of x is should have been 3/√2 in the initial equation.
P: 37
 Quote by eumyang I'm getting the same roots (-2.80 and 0.80). When I played around with the coefficients of the original quadratic, I found that if you made the coefficient of the x2 term 2k: 2kx2 - 3x + (k+2) = 0 You will get the original answer that you stated: -2.4577 < k < 0.4577. So it looks like either you copied the problem incorrectly or the book has a typo somewhere.
I guess everyone makes mistakes.. it gets extremely annoying when textbooks provide you with the wrong answers or have a typo.
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 Quote by thornluke I guess everyone makes mistakes.. it gets extremely annoying when textbooks provide you with the wrong answers or have a typo.