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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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Math Expert
Joined: 02 Sep 2009
Posts: 43792
If one of the roots of the quadratic equation x^2 + mx + 24 = 0 is 1.5 [#permalink]

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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
[Reveal] Spoiler: OA

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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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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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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

$$1.5*m$$ =$$- 26.25$$

$$m$$ =$$-17.5$$

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Joined: 28 Mar 2016
Posts: 5
Re: If one of the roots of the quadratic equation x^2 + mx + 24 = 0 is 1.5 [#permalink]

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15 Jun 2016, 03:06
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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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Joined: 18 Jan 2010
Posts: 256
Re: If one of the roots of the quadratic equation x^2 + mx + 24 = 0 is 1.5 [#permalink]

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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

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Posts: 13840
Re: If one of the roots of the quadratic equation x^2 + mx + 24 = 0 is 1.5 [#permalink]

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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   [#permalink] 15 Oct 2017, 04:39
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