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

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New post 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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New post 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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New post 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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New post 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

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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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