A given quadratic equation ax^2 52x + 24 = 0 has 13/6 as sum of the

Question

A given quadratic equation  ax^2 – 52x + 24 = 0  has  \frac{13}{6}  as sum of the roots. Find the product of the roots.

(A)  24

(B)  1

(C)  12

(D)  \frac{24}{5}

(E)  2

CareerGeek · Answer

For the quadratic equation,  ax^2 + bx + c = 0 ,
Sum of the roots =  -\frac{b}{a}  & product of the roots =  \frac{c}{a}

For the given equation,  ax^2 - 52x + 24 = 0 ,
Sum of the roots =  \frac{13}{6} 
-->  -\frac{(-52)}{a} = \frac{13}{6} 
-->  a = 52*\frac{6}{13} = 24

--> Product of the roots =  \frac{c}{a} = \frac{24}{24} = 1

IMO Option B

freedom128 · Answer

Root: x1, x2
x1+x2= -(-52/a) = 13/6 --> a=24
x1.x2= 24/a = 24/24 = 1

FINAL ANSWER IS (B)

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lacktutor · Answer

A given quadratic equation 
 ax^{2}—52x+ 24= 0  has  \frac{13}{6}  as sum of the roots. 
—> Find the product of the roots???

Sum of the roots:
  x_1+ x_2= —\frac{b}{a} 
—>  x_1+ x_2= —(—\frac{52}{a}) = \frac{13}{6}  
—> a = 24

24x^{2} —52x+ 24 =0

Product of the roots: 
 x_1*x_2= \frac{c}{a}=\frac{24}{24}= 1

The answer is B

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Jawad001 · Answer

Sum of the roots = -b/a
Products of the roots = c/a
-b/a = 13/6
-(-52/a) = 13/6
52/a = 13/6
 a = 24
Products of the roots = c/a
c/a = 24/24
 = 1(B)

Archit3110 · Answer

sum =-b/a & product = c/a
ax^2+bx+c=0
given 
ax^2–52^x+24=0
52/a = 13/6 
a= 24
product = 24/24 ; 1
IMO B

A given quadratic equation ax2–52x+24=0 has 13/6 as sum of the roots. Find the product of the roots.

(A) 24

(B) 1

(C) 12

(D) 24/5

(E) 2

unraveled · Answer

A given quadratic equation  ax^2–52x+24=0  has  \frac{13}{6}  as sum of the roots. Find the product of the roots.

(A) 24
(B) 1
(C) 12
(D)  \frac{24}{5} 
(E) 2

From  ax^2–52x+24=0  we have a = a, b = -52 and c = 24 
 \frac{13}{6} = -\frac{b}{a}  = sum of roots
 \frac{13}{6} = -\frac{-52}{a}  
a = 24

So, Product of roots =  \frac{c}{a} 
=  \frac{24}{24} 
=1

Answer B.

eakabuah · Answer

Given that the sum of roots of the quadratic equation ax^2–52x+24=0 is 13/6, we are to determine the product of the roots.
A quadratic equation can be written as x^2 - (sum of roots)x + (product of roots) = 0
The quadratic equation above can be rewritten as: x^2–52x/a+24/a=0
sum of roots = 52/a = 13/6
Hence a = 24.
This implies the product of roots = 24/24 = 1.

The answer is B.

joohwangie · Answer

A given quadratic equation ax2–52x+24=0ax2–52x+24=0 has 13/6 as sum of the roots. Find the product of the roots.

(A) 24

(B) 1

(C) 12

(D) 24/5

(E) 2

by looking at the answer choices the roots must be the same sign since the product yield out a positive number.
and the sum added up to 13/6 therefore those roots are both positive.

we assume random 2 positive numbers that added up to 13/6

5/6+8/9 then the product is 20/13 none in the answer choices
7/6+6/6 then the product is 7/6 none in the answer choices 
4/6+9/6 then the product is 1

Therefore B

QuantMadeEasy · Answer

General form of quadratic equation ax^2 + bx + c =0
Sum of the roots is -b/a and product of the root is c/a

According to questions
52/a = 13/6
a = 24

Product of the roots = c/a = 24/24 = 1

B is correct

doomedcat · Answer

sum of roots of quadratic equation = -b/a
given 13/6= 52/a; a= 24

product of roots for quadratic eqtn = c/a
24/24
=1

ans B

PoojanB · Answer

comparing eqn with standard form ax^2+bx+c=0,
a=a,b=52,c=24

sum of root =-b/a=13/6 given
 = 13/6=-(-52/a),solving it will give a=24
product of root= c/a=24/24=1

Ans B

bumpbot · Answer

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A given quadratic equation ax^2 52x + 24 = 0 has 13/6 as sum of the

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A given quadratic equation ax^2 52x + 24 = 0 has 13/6 as sum of the

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