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What is the product of the roots of the equation x^2 - 4x + k = 3 ?

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Bunuel
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What is the product of the roots of the equation x^2 - 4x + k = 3 ? [#permalink] New post   18 Jan 2022, 02:30
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What is the product of the roots of the equation \(x^2 - 4x + k = 3\) ?

(1) One of the roots of the equation \(x^2 - 4x + k = 3\) is 1

(2) \(k = 6\)


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D
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What is the product of the roots of the equation x^2 - 4x + k = 3 ? [#permalink] New post   Updated on: 18 Jan 2022, 03:51
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Bunuel wrote:
What is the product of the roots of the equation \(x^2 - 4x + k = 3\) ?

(1) One of the roots of the equation \(x^2 - 4x + k = 3\) is 1

(2) \(k = 6\)


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Equation: x^2 - 4x + k = 3

Can be rewritten as x^2 - 4x + k-3 = 0

So product of the equation = c/a = k-3/1. | c= k-3 a =1

So basically we need the value of K.

(1) One of the roots of the equation \(x^2 - 4x + k = 3\) is 1
Let the other root be R.
Sum of the roots = -b/a = 4
One root is 1
So, 1+ R = 4
R = 3
Product = 3.
Sufficient.

(2) \(k = 6\)
We are getting the value of K, we can find out the product of the roots.

Sufficient.

D is the answer.

Originally posted by ElninoEffect on 18 Jan 2022, 03:20.
Last edited by ElninoEffect on 18 Jan 2022, 03:51, edited 1 time in total.
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Re: What is the product of the roots of the equation x^2 - 4x + k = 3 ? [#permalink] New post   18 Jan 2022, 03:42
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1) Tells us that one root of \(x^2 - 4x + k = 3\) is 1.

For the form \(ax^2 + bx + c\), the sum of the roots will equal \(-b\). If one of the roots is 1, then we know that after factorising the quadratic we will have a bracket with \((x - 1)\). As the sum of the roots must equal to \(-b\), the other root will have to be \(3\).

With the roots being 1 and 3, their product will be \(3\)

SUFFICIENT


2) Plugging in k = 6 into \(x^2 - 4x + k = 3\) gives:

\(x^2 - 4x + 6 = 3\)

\(x^2 - 4x + 3 = 0\)

\((x - 3)(x - 1)\)

x = 3 or x = 1

Product of roots: \(3*1 = 3\)

SUFFICIENT

Answer D
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Re: What is the product of the roots of the equation x^2 - 4x + k = 3 ? [#permalink] New post   18 Jan 2022, 06:12
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Pre-thinking
For x^2 - 4x + (k-3) = 0
x1*x2 = (k-3) / 1 = k - 3.
In order to answer the question, we need to know the value of k.

(1) So 1^2 - 4*1 + k = 3 => 1-4+k=3 => k=6
Sufficient.

(2) k=6
Sufficient

Answer is (D).
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Re: What is the product of the roots of the equation x^2 - 4x + k = 3 ? [#permalink] New post   18 Jan 2022, 11:32
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What is the product of the roots of the equation \(x^2 - 4x + k = 3\) ?

a+b = 4 and a*b = k-3, where a and b are two roots of the equations.

Stat1: One of the roots of the equation \(x^2 - 4x + k = 3\) is 1
if a = 1 then b= 3 and a*b = 3. Sufficient

Stat2: \(k = 6\)
then, a*b = 6-3 = 3 Sufficient

So, I think D. :)
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Re: What is the product of the roots of the equation x^2 - 4x + k = 3 ? [#permalink]
18 Jan 2022, 11:32
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Bunuel
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