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If z=9/2 is a solution of the equation 2z²+kz-30=6, find:

a) the value of k

b) the other solution of the equation

I appreciate any form of help, thank you

Guest Sep 5, 2017

#1
+26489
+2

a)  Substitute 9/2 for z in the equation:

2*(9/2)2 + k*9/2 - 30 = 6

81/2 + 9k/2 = 36

81 + 9k = 72

9k = -9

k = -1

b) Use this value of k in the original equation:

2z2 - z -30 = 6

2z2 - z -36 = 0

z2 - z/2 -18 = 0

(z + 4)(z - 9/2) = 0

The other solution is therefore z = -4

.

Alan  Sep 5, 2017
Sort:

#1
+26489
+2

a)  Substitute 9/2 for z in the equation:

2*(9/2)2 + k*9/2 - 30 = 6

81/2 + 9k/2 = 36

81 + 9k = 72

9k = -9

k = -1

b) Use this value of k in the original equation:

2z2 - z -30 = 6

2z2 - z -36 = 0

z2 - z/2 -18 = 0

(z + 4)(z - 9/2) = 0

The other solution is therefore z = -4

.

Alan  Sep 5, 2017

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