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If one of the roots of the quadratic equation x^2 + mx + 24 = 0 is 1.5

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If one of the roots of the quadratic equation x^2 + mx + 24 = 0 is 1.5  [#permalink]

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New post 14 Mar 2016, 06:29
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If one of the roots of the quadratic equation x^2 + mx + 24 = 0 is 1.5, then what is the value of m?

A. -22.5
B. -17.5
C. -10.5
D. 16
E. Cannot be determined

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Re: If one of the roots of the quadratic equation x^2 + mx + 24 = 0 is 1.5  [#permalink]

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New post 14 Mar 2016, 23:33
Bunuel wrote:
If one of the roots of the quadratic equation x^2 + mx + 24 = 0 is 1.5, then what is the value of m?

A. -22.5
B. -17.5
C. -10.5
D. 16
E. Cannot be determined


Here X=1.5 must satisfy the equation
Hence => 1.5^2 +1.5m +24 =0
hence m=-17.5
So B
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If one of the roots of the quadratic equation x^2 + mx + 24 = 0 is 1.5  [#permalink]

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New post 15 Jun 2016, 02:35
For a quadratic equation if a root is given it satisfies the given equation
In equation \(x^2\)\(+\)\(mx\)\(+\)\(24\) = 0 substitute \(x\)=1.5

\(1.5^2\)\(+\)\(1.5*m\)\(+\)\(24\) = 0

\(1.5*m\) =\(- 26.25\)

\(m\) =\(-17.5\)

Correct Answer - B
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Re: If one of the roots of the quadratic equation x^2 + mx + 24 = 0 is 1.5  [#permalink]

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New post 15 Jun 2016, 03:06
1
Bunuel wrote:
If one of the roots of the quadratic equation x^2 + mx + 24 = 0 is 1.5, then what is the value of m?

A. -22.5
B. -17.5
C. -10.5
D. 16
E. Cannot be determined


Alternate Way of solving this question.



Product of roots of quadratic equation \((ax^2 + bx +c = 0)\) is \(\frac{c}{a}\)
\(r_1 * r_2 = \frac{c}{a}\)
\(1.5 * r_2 = \frac{24}{1}\)
\(r_2 = 16\)

Also Sum of roots of quadratic equation \((ax^2 + bx +c = 0)\) is \(\frac{-b}{a}\)
\(r_1 + r_2 =\frac{-b}{a}\)
\(1.5 + 16 = \frac{-m}{1}\)
\(m = -17.5\)


\(Answer = B\)
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Re: If one of the roots of the quadratic equation x^2 + mx + 24 = 0 is 1.5  [#permalink]

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New post 15 Jun 2016, 03:19
Bunuel wrote:
If one of the roots of the quadratic equation x^2 + mx + 24 = 0 is 1.5, then what is the value of m?

A. -22.5
B. -17.5
C. -10.5
D. 16
E. Cannot be determined


(Formula is sum of roots = -(b/a); Product of roots is (c/a), where equation is (a.\(x^2\)+bx+c = 0)

Here say roots are 1.5 and z


1.5+z = -m -------------(1)
1.5z = 24 ---------------(2)

From (2), z = 24/1.5 = 16

- m = 16+1.5 = 17.5

m = -17.5

B is the answer.
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Re: If one of the roots of the quadratic equation x^2 + mx + 24 = 0 is 1.5  [#permalink]

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New post 15 Oct 2017, 04:39
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Re: If one of the roots of the quadratic equation x^2 + mx + 24 = 0 is 1.5 &nbs [#permalink] 15 Oct 2017, 04:39
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