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If (x - 6)(x - m) = x^2 + rx + k. What is the value of m?

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Bunuel
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If (x - 6)(x - m) = x^2 + rx + k. What is the value of m? [#permalink] New post   04 Jun 2018, 11:05
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If \((x - 6)(x - m) = x^2 + rx + k\). What is the value of m?


(1) \(k = 18\)

(2) \(r = -9\)
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D
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BrentGMATPrepNow
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Re: If (x - 6)(x - m) = x^2 + rx + k. What is the value of m? [#permalink] New post   04 Jun 2018, 11:16
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Bunuel wrote:
If \((x - 6)(x - m) = x^2 + rx + k\), what is the value of m?


(1) \(k = 18\)

(2) \(r = -9\)


Sweet question, Bunuel!!

Target question: What is the value of m?

Given: (x - 6)(x - m) = x² + rx + k
Use F.O.I.L. to expand left side: x² - mx - 6x + 6m = x² + rx + k
Rewrite left side as follows: x² + (-m - 6)x + 6m = x² + rx + k

This tells us two things:
-m - 6 = r
6m = k

Now onto the statements!!

Statement 1: k = 18
We already know that 6m = k
This means: 6m = 18
So, m = 3
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: r = -9
We already know that -m - 6 = r
This means: -m - 6 = -9
Solve to get: m = 3
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent
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Re: If (x - 6)(x - m) = x^2 + rx + k. What is the value of m? [#permalink] New post   04 Jun 2018, 22:14
Bunuel wrote:
If \((x - 6)(x - m) = x^2 + rx + k\). What is the value of m?


(1) \(k = 18\)

(2) \(r = -9\)



Statement(1):-

Let's put the value of k in the given quadratic equation, we have

\(x^2\)-(6+m)x+6m= \(x^2\)+rx+18

Now equating the constant terms in both the sides of quadratic equation we have,

6m=18 or m=3.

Therefore, Statement(1) is sufficient.

Statement(2):-

Let's put the value of r in the given quadratic equation, we have

\(x^2\)-(6+m)x+6m= \(x^2\)+(-9)x+k

Now equating the co-efficient x in both the sides of quadratic equation we have,

-(6+m)=-9
or, m=3

Therefore, Statement(2) is sufficient.

Hence, answer option(D)
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Re: If (x - 6)(x - m) = x^2 + rx + k. What is the value of m? [#permalink] New post   04 Jun 2018, 22:29
Bunuel wrote:
If \((x - 6)(x - m) = x^2 + rx + k\). What is the value of m?


(1) \(k = 18\)

(2) \(r = -9\)


Simplifying the equation:

x^2 - mx - 6x +6m=x^2+rx+k
=> (-m-6)x+6m=rx+k
Statement 1: if k=18, then from the above equation, 6m=18 => m=3 Sufficient
Statement 2: if r=9, then from the above equation, (-m-6)=9 => m=3 - Sufficient

Therefore Answer is D.
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Re: If (x - 6)(x - m) = x^2 + rx + k. What is the value of m? [#permalink] New post   15 Feb 2022, 19:49
Given the following form of a quadratic equation:

a(x)^2 + b(x) + c

(1) the SUM of the Roots of the quadratic is given by = -(b) / (a)

(2) the PRODUCT of the Roots of the quadratic is given by = (c) / (a)

The ROOTS of the quadratic are the values of the Input (here X) that make the quadratic equal 0

We are given the factored form of the quadratic as:

(x - 6) (x - m)

The ROOTS are therefore: x = 6 …..and…. x = m

SUM of Roots = (6 + m) = -(r)

PRODUCT of Roots = (6) (m) = k

What is the value of m = ?

D - each statement is sufficient alone as we can plug in the value of k or r and find that

m = 3

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Re: If (x - 6)(x - m) = x^2 + rx + k. What is the value of m? [#permalink]
15 Feb 2022, 19:49
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Bunuel
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