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(2x+5)(-mx+9)=0
in the given equation, m is the constant has the solutions
x= -5/2 and x=3/2, whats the value of m?

2x5mx90 in the given equation m is the constant has the solutions x 52 and x32 whats the value of m class=

Respuesta :

msm555

Answer:

[tex]\boxed{\sf -\dfrac{18}{5}}[/tex].

Step-by-step explanation:

In the given equation [tex]\sf (2x + 5)(-mx + 9) = 0[/tex], the solutions [tex]\sf x = -\dfrac{5}{2}[/tex] and [tex]\sf x = \dfrac{3}{2}[/tex] indicate the values of [tex]\sf x[/tex] that make the equation true.

To find the value of [tex]\sf m[/tex], we can set each factor equal to zero and solve for [tex]\sf m[/tex]:

1. Set [tex]\sf 2x + 5[/tex] equal to zero:

[tex]\sf 2x + 5 = 0[/tex]

Solve for [tex]\sf x[/tex]:

[tex]\sf 2x = -5[/tex]

[tex]\sf x = -\dfrac{5}{2}[/tex]

2. Set [tex]\sf -mx + 9[/tex] equal to zero:

[tex]\sf -mx + 9 = 0[/tex]

Solve for [tex]\sf x[/tex]:

[tex]\sf -mx = -9[/tex]

[tex]\sf x = \dfrac{9}{m}[/tex]

Now, compare the values of [tex]\sf x[/tex] from the solutions:

[tex]\sf x = -\dfrac{5}{2} \quad \text{and} \quad x = \dfrac{9}{m}[/tex]

Since these are the same solutions, we can set them equal to each other:

[tex]\sf -\dfrac{5}{2} = \dfrac{9}{m}[/tex]

Now, solve for [tex]\sf m[/tex]:

[tex]\sf m = -\dfrac{9}{\dfrac{5}{2}} = -\dfrac{9}{1} \times \dfrac{2}{5} \\\\ = -\dfrac{18}{5}[/tex]

So, the value of [tex]\sf m[/tex] is [tex]\boxed{\sf -\dfrac{18}{5}}[/tex].

semsee45

Answer:

m = 6

Step-by-step explanation:

The given equation (2x + 5)(-mx + 9) = 0 is a quadratic equation in factored form.

The solutions of such an equation are the values of x that make each factor equal to zero. Therefore, to find the solutions of the given equation, we need to set each factor to zero and solve for x:

[tex]\boxed{\begin{aligned}\underline{\sf Factor\;1}\\\\2x+5&=0\\\\2x+5-5&=0-5\\\\2x&=-5\\\\\drac{2x}{2}&=\dfrac{-5}{2}\\\\x&=-\dfrac{5}{2}\end{aligned}}[/tex]       [tex]\boxed{\begin{aligned}\underline{\sf Factor\;2}\\\\-mx+9&=0\\\\-mx+9-9&=0-9\\\\-mx&=-9\\\\\dfrac{-mx}{-m}&=\dfrac{-9}{-m}\\\\x&=\dfrac{9}{m}\end{aligned}}[/tex]

Given that the solutions are x = -5/2 and x = 3/2, this means that the solution of the second factor (9/m) must be equal to 3/2. Therefore:

[tex]\dfrac{9}{m}=\dfrac{3}{2}[/tex]

To find the value of m, cross-multiply:

[tex]\begin{aligned}9 \cdot 2&=3 \cdot m\\\\18&=3m\end{aligned}[/tex]

Now, divide both sides by 3:

[tex]\begin{aligned}\dfrac{18}{3}&=\dfrac{3m}{3}\\\\6&=m\end{aligned}[/tex]

Therefore, the value of m is:

[tex]\huge\boxed{\boxed{m=6}}[/tex]

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