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How many and what type of solutions does the equation have?
5y^2=18y−4

a) two rational solutions
b)two nonreal solutions
c)two irrational solutions
d)one rational solution

Respuesta :

ghanami
hello:
5y²=18y−4
5y²-18y+4 = 0
delta = (-18)²-4(5)(4) = 244 
(delta) >  0
( c)two irrational solutions because 244 is not a perfect number

Using the discriminant of the quadratic equation, it is found that the correct option regarding the number and the type of solutions that the equation has is:

c) two irrational solutions

What is a quadratic function?

A quadratic function is given according to the following rule:

[tex]y = ax^2 + bx + c[/tex]

The discriminant is:

[tex]\Delta = b^2 - 4ac[/tex]

The solutions are dependent on the discriminant, as follows:

  • If [tex]\mathbf{\Delta > 0}[/tex], y has two solutions. If the discriminant is a perfect square, the solutions are rational, otherwise they are irrational.
  • If [tex]\mathbf{\Delta = 0}[/tex], y has one rational solutions.
  • If [tex]\mathbf{\Delta < 0}[/tex], y has two nonreal solutions.

In this problem, the equation is:

[tex]5y^2 = 18y - 4[/tex]

[tex]5y^2 - 18y + 4[/tex]

Hence, the coefficients are [tex]a = 5, b = -18, c = 4[/tex], and the discriminant is:

[tex]\Delta = (-18)^2 - 4(5)(4) = 244[/tex]

244 a positive number, however it is not a perfect square, hence the equation has two irrational solutions, and option C is correct.

You can learn more about the discriminant of a quadratic equation at https://brainly.com/question/19776811

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