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If 4 is one solution of the equation x^2 + 3x + k = 10, wher
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16 Jun 2020, 03:31
16 Jun 2020, 03:31
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20% (01:11) wrong based on 68 sessions
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If 4 is one solution of the equation \(x^2 + 3x + k = 10\), where k is a constant, what is the other solution?
(A) -7
(B) -4
(C) -3
(D) 1
(E) 6
(A) -7
(B) -4
(C) -3
(D) 1
(E) 6
Re: If 4 is one solution of the equation x^2 + 3x + k = 10, wher
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16 Jun 2020, 03:32
16 Jun 2020, 03:32
Expert Reply
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
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Re: If 4 is one solution of the equation x^2 + 3x + k = 10, wher
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16 Jun 2020, 05:20
16 Jun 2020, 05:20
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Carcass wrote:
If 4 is one solution of the equation \(x^2 + 3x + k = 10\), where k is a constant, what is the other solution?
(A) -7
(B) -4
(C) -3
(D) 1
(E) 6
(A) -7
(B) -4
(C) -3
(D) 1
(E) 6
Let's first determine the value of k.
Since x = 4 is a solution to the equation x² + 3x + k = 10, we know that x = 4 SATISFIES the equation.
That is: 4² + 3(4) + k = 10
Evaluate to get: 16 + 12 + k = 10
Solve for k to get: k = -18
So, the ORIGINAL equation is x² + 3x + (-18) = 10
This is the same as: x² + 3x - 18 = 10
We now need to solve this equation.
First, set it equal to zero: x² + 3x - 28 = 0
Factor: (x + 7)(x - 4) = 0
So, x = -7 or x = 4
We already know that x = 4 is one solution.
So, the other solution is x = -7
Answer: A
Cheers,
Brent
