If 3 is one of the roots of x^2 - 5x +2k = 13, what is the product of

Question

If 3 is one of the roots of x^2 - 5x +2k = 13, what is the product of the two roots of the equation?

(A) -12
 (B) -6
 (C) 5
(D) 6
(E) 12

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ravi1522 · Answer

Hello,
As 3 is one the root so we can use x=3 to find value of k
x^2 - 5x +2k = 13
9-15+2k=13
2k=19
x^2 - 5x +19 - 13=0
x^2 - 5x +6=0
product of root will be c/a
Hence,
Option D
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overclockedboi · Answer

If 3 is one of the roots of  x^2 - 5x +2k = 13 , it implies that  x=3  will satisfy the equation.

Hence,  x^2 - 5x +2k = 13  = >  3^2 - (5*3) + 2k = 13

i.e.,

9 - 15 + 2k = 13 ,

Hence,  2k = 19

Now, product of of two roots of a quadratic equation  ax^2+bx+c = 0  is given by  \frac{c}{a}

So,  \frac{c}{a} = \frac{(2k-13)}{1}  =>  \frac{c}{a} = 6

Hence, D.

charlie1195 · Answer

Alternate approach (we don't have to find the value to k)

Given eq. -> x^2 - 5x +2k = 13
We know that sum of roots of an equation is given by -b/a, 
Let the two roots be x1 and x2
x1 + x2 = -b/a
a = 1; b = -5; x1 = 3 (given)
3 + x2 = -(-5)/1 ---> x2 = 2

We now know that the values of x1 and x2 are 3 and 2, hence the product = 3*2 = 6

Answer => D

hr1212 · Answer

x^2 - 5x + 2k = 13

Sum of roots = 5
3 + other root = 5
other root = 2

Product = 3*2 = 6

IMO: D

sujoykrdatta · Answer

x^2 - 5x +2k = 13 => x^2 - 5x +2k - 13 = 0
The expression we want to factorise is: y = x^2 - 5x + (2k - 13)
Since this has a root 3, (x - 3) is a factor. 
If the other root be r, the factor would be (x - r)
=> y = x^2 - 5x + (2k - 13) = (x - 3)(x - r) ... this is true for all values of x
=> x^2 - 5x + (2k - 13) = x^2 - x(r + 3) + 3r

Comparing the coefficient of x on both sides: -5 = -(r + 3) => r = 2
 => Product of roots = 3 * 2 = 6  Answer D

Point to note: For y = ax^2 + bx + c: Sum of roots = -b/a and Product of roots = c/a

Whoisdmx15 · Answer

Sum of Roots = -coeff of x/coeff of x^2. Therefore 3 + Root 2 = 5, Therefore Root 2 = 2. Hence product of roots is 6.

AVMachine · Answer

aX^2 + bx + c = 0;

Have, Sum of Roots = -b/a; and Product of Roots= c/a;

x^2 -5x + 2k = 13;

x^2 -5x + 2k - 13 = 0; a = 1; b = -5; c = 2k-13

-b/a = +5; if one root is three then the other must be 2;

And product of 3 & 2 is 6;

Ans: D

S1mple3 · Answer

sum of roots = 5, therefore other root will be 2.

Hence answer, 3*2 =6

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If 3 is one of the roots of x^2 - 5x +2k = 13, what is the product of

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If 3 is one of the roots of x^2 - 5x +2k = 13, what is the product of

Prep Toolkit

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