Respuesta :

mhanifa

Answer:

  • c = 3.09375

Step-by-step explanation:

Standard for of quadratic equation:

  • ax² + bx + c = 0

We have

  • 2x² - 5x + c = 0

Sum of the roots

  • x₁ + x₂ = - b/a = -(-5)/2 = 2.5

Product of the roots

  • x₁x₂ = c/a = c / 2

We have:

  • x₁ - x₂ = 0.25

The square of the above is:

  • (x₁ - x₂)² = (x₁ + x₂)² - 4x₁x₂

Substitute known values and solve for c:

  • 0.25² = (2.5)² - 4(c/2)
  • 2c = 6.25 - 0.0625
  • 2c = 6.1875
  • c = 3.09375
semsee45

Answer:

c = 3.09375

Step-by-step explanation:

Factored form of a quadratic equation

[tex]y=a(x-r_1)(x-r_2)[/tex]

where:

  • a is the leading coefficient
  • [tex]r_1[/tex] and [tex]r_2[/tex] are the roots

Given quadratic:

[tex]2x^2-5x+c=0[/tex]

Therefore, the leading coefficient is:

[tex]\implies a=2[/tex]

Substitute the value of a into the formula:

[tex]\implies y=2(x-r_1)(x-r_2)[/tex]

Expand:

[tex]\implies y=2x^2-(2r_2+2r_1)x+2r_1r_2[/tex]

Compare the coefficients of x:

[tex]\implies -(2r_2+2r_1)=-5[/tex]

[tex]\implies 2r_2+2r_1=5[/tex]

[tex]\implies r_2+r_1=2.5[/tex]

If the difference between the roots is 0.25 then:

[tex]\implies r_2-r_1=0.25[/tex]

Add the two root equations to eliminate r₁:

[tex]\implies 2r_2=2.75[/tex]

[tex]\implies r_2=1.375[/tex]

Substitute the found value of r₂ into one of the root equations and solve for r₁:

[tex]\implies 1.375-r_1=0.25[/tex]

[tex]\implies r_1=1.375-0.25[/tex]

[tex]\implies r_1=1.125[/tex]

As c = 2r₁r₂ then:

[tex]\implies c=2(1.125)(1.375)[/tex]

[tex]\implies c=3.09375[/tex]

Learn more about factored quadratics here:

https://brainly.com/question/27783166

https://brainly.com/question/27934929

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