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If one root of the equation 2x^2 + 3x - k = 0 is 6...

This topic has 2 expert replies and 0 member replies

If one root of the equation 2x^2 + 3x - k = 0 is 6...

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If one root of the equation 2x^2 + 3x - k = 0 is 6, what is the value of k?

(A) 90
(B) 42
(C) 18
(D) 10
(E) -10

The OA is A.

Please, can any expert explain this PS question for me? I tried to solve it of the following way,

If one root is 6, then I can say that 2*6^2 + 3*6 - k=0 and isolate k and get it value, right? . Thanks.

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Quote:
If one root of the equation 2x² + 3x - k = 0 is 6, what is the value of k?

(A) 90
(B) 42
(C) 18
(D) 10
(E) -10
Hi Swerve,
Let's take a look at your question.

6 is the root of the quadratic equation 2x² + 3x - k = 0, therefore,
$$2\left(6\right)^2+3\left(6\right)-k=0$$
$$2\left(36\right)+3\left(6\right)-k=0$$
$$72+18-k=0$$
$$90-k=0$$
$$k=90$$

Therefore, Option A is correct.

Hope it helps.
I am available if you'd like any follow up.

_________________
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swerve wrote:
If one root of the equation 2x² + 3x - k = 0 is 6, what is the value of k?

(A) 90
(B) 42
(C) 18
(D) 10
(E) -10
Your suggested approach is perfect. Here's how it might go...

Since x = 6 is a solution, we know that it SATISFIES the equation 2x² + 3x - k = 0
So, plug x = 6 into the equation to get: 2(6)² + 3(6) - k = 0
Simplify: 72 + 18 - k = 0
Solve to get: k = 90

Answer: A

Cheers,
Brent

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