Leah Rose P.

asked • 07/28/15# Find k in the equation

Find k in the equation (k-3)x

^{2}+ (k-2)x - 5so that:

a) the sum of roots is 3.

b) the product of roots is -4.

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## 1 Expert Answer

**The sum of the roots of Ax**

^{2}+ Bx + C = 0 is -B/A and the product of the roots is C/A.**(a). If (k-3)x**

^{2}+ (k-2)x - 5 = 0 and if the sum of the roots is 3, then -(k-2)/(k-3) = 3**Therefore, -k + 2 = 3k - 9**

**4k = 11 k = 11/4**

**(b). If the product of the roots is -4, then -5/(k-3) = -4**

**So, -4k +12 = -5**

**-4k = -17 k = 17/4**

Leah Rose P.

Hello Mark, it is okay if there are two different solutions to k? Because when they are substituted to the original equation, it gives different results of sum and product of the roots. I am expecting your fast reply. Thank you

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07/29/15

Mark M.

tutor

**I think that (a) and (b) are separate problems. There is no value of k for which (a) and (b) are true simultaneously.**

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07/29/15

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Mark M.

07/28/15