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

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Director
Joined: 18 Feb 2019
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GMAT 1: 460 Q42 V13
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What is the product of the roots of the equation x^2-4x+k=3  [#permalink]

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08 May 2019, 10:49
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What is the product of the roots of the equation x^2-4x+k=3

I. One of the roots of the equation x2 - 4x + k = 3 is 1

II. k = 6
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What is the product of the roots of the equation x^2-4x+k=3  [#permalink]

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08 May 2019, 19:21
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kiran120680 wrote:
What is the product of the roots of the equation $$x^2-4x+k=3$$

I. One of the roots of the equation $$x^2 - 4x + k = 3$$ is 1

II. k = 6

General form of a quadratic eq when the roots are known: $$x^2-Sx+P=0$$, where S=Sum of the roots & P=Product of the roots.

Re-arranging the given equation, $$x^2-4x+(k-3)=0$$

Question stem:- P=k-3? or, k=?

St1:- Since 1 is one of the roots of the given QE, hence $$1^2 - 4*1 + k = 3$$.
Value of k can be determined.
Sufficient.

St2:- k=6. Sufficient.

Ans. (D)
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Re: What is the product of the roots of the equation x^2-4x+k=3  [#permalink]

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16 Jun 2019, 12:56
Apply Viet's theorem
+Re-arranging the equation: x^2-4x+k=3--> x^2-4x+k-3=0
St1:One of the roots of the equation x2 - 4x + k = 3 is 1
x1=1
According to Viet's theorem, we have x1 + x2 = -(b/a)-->x2= 4 - 1= 3
x1*x2= 1*3= 3
----->Sufficient

St2: k = 6
With this info, we can complete the equation and find its roots
-->Sufficient
So, both statement are sufficient---->D
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Re: What is the product of the roots of the equation x^2-4x+k=3  [#permalink]

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16 Jun 2019, 13:32
kiran120680 wrote:
What is the product of the roots of the equation x^2-4x+k=3

I. One of the roots of the equation x2 - 4x + k = 3 is 1

II. k = 6

I. One of the roots of the equation x2 - 4x + k = 3 is 1
—> 1 satisfies the quadratic equation
—> 1^2 - 4*1 + k = 3
—> k = 6

Substitute the value of k in the quadratic equation
—> x^2 - 4x + 6 = 3
—> x^2 - 4x + 3 = 0
—> (x - 3)(x - 1) = 0

The roots are 3 & 1
Product of the roots = 3

—> Sufficient

II. k = 6
—> x^2 - 4x + 6 = 3
**Same as above

Sufficient

IMO Option D

Alternate Method

Formula: For any given quadratic equation
ax^2 + bx + c = 0
Sum of the roots = -b/a
Product of the roots = c/a

I. One of the roots of the equation x2 - 4x + k = 3 is 1
—> x^2 - 4x + (k - 3) = 0
Let the roots be m & 1

Sum of the roots = -b/a = -(-4)/1 = 4
—> m + 1 = 4
—> m = 3

Product of the roots = m*1 = m = 3

Sufficient

II. k = 6
—> x^2 - 4x + 6 = 3
—> x^2 - 4x + 3 = 0

Product of the roots = c/a = 3/1 = 3

Sufficient

IMO Option D

Pls Hit kudos if you like the solution

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Re: What is the product of the roots of the equation x^2-4x+k=3   [#permalink] 16 Jun 2019, 13:32
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