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

Question

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

stonecold · Answer

Here X=1.5 must satisfy the equation
Hence => 1.5^2 +1.5m +24 =0
hence m=-17.5
So B

rhine29388 · Answer

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

JD01 · Answer

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

adiagr · Answer

(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.

Basshead · Answer

Quadratic formula:  ax^2 + bx + c = 0

Product of roots:  \frac{c}{a}

Sum of roots =  \frac{-b}{a}

We're given one of the roots is 1.5

1.5 * root2 = 24/1
root2 = 16

Sum of roots:

1.5 + 16 = \frac{-b}{a} 
 \frac{-b}{a}  = -17.5

Answer is B.

ScottTargetTestPrep · Answer

Solution:
 
Substituting 1.5 for x, we have:

1.5^2 + 1.5m + 24 = 0

2.25 + 1.5m + 24 = 0

1.5m = -26.25

m = -17.5

Answer: B

bumpbot · Answer

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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

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