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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 [#permalink] New post   10 Jan 2020, 02:14
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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) \(2\)


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Re: A given quadratic equation ax^2 – 52x + 24 = 0 has 13/6 as sum of the [#permalink] New post   10 Jan 2020, 02:31
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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
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Re: A given quadratic equation ax^2 – 52x + 24 = 0 has 13/6 as sum of the [#permalink] New post   10 Jan 2020, 03:15
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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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Re: A given quadratic equation ax^2 – 52x + 24 = 0 has 13/6 as sum of the [#permalink] New post   10 Jan 2020, 04:00
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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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Re: A given quadratic equation ax^2 – 52x + 24 = 0 has 13/6 as sum of the [#permalink] New post   10 Jan 2020, 04:21
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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)
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Re: A given quadratic equation ax^2 – 52x + 24 = 0 has 13/6 as sum of the [#permalink] New post   10 Jan 2020, 09:51
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
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Re: A given quadratic equation ax^2 – 52x + 24 = 0 has 13/6 as sum of the [#permalink] New post   10 Jan 2020, 12:02
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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.
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Re: A given quadratic equation ax^2 – 52x + 24 = 0 has 13/6 as sum of the [#permalink] New post   10 Jan 2020, 17:16
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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.
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Re: A given quadratic equation ax^2 – 52x + 24 = 0 has 13/6 as sum of the [#permalink] New post   11 Jan 2020, 21:01
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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
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Re: A given quadratic equation ax^2 – 52x + 24 = 0 has 13/6 as sum of the [#permalink] New post   11 Jan 2020, 21:44
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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
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Re: A given quadratic equation ax^2 – 52x + 24 = 0 has 13/6 as sum of the [#permalink] New post   12 Jan 2020, 02:16
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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
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Re: A given quadratic equation ax^2 – 52x + 24 = 0 has 13/6 as sum of the [#permalink] New post   12 Jan 2020, 10:09
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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
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Re: A given quadratic equation ax^2 – 52x + 24 = 0 has 13/6 as sum of the [#permalink] New post   27 Mar 2021, 17:34
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