Respuesta :

luisejr77

Answer: Two distinct real roots.

Step-by-step explanation:

Given a quadratic equation [tex]ax^2+bx+c=0[/tex], we can predict the type of solution by calculating the Discriminant (D):

[tex]D=b^2-4ac[/tex]

Identify a, b and c from [tex]5x^2- 2x-3=0[/tex].

[tex]a=5\\b=-2\\c=-3[/tex]

Substitute into the formula of the Discriminant. Then:

[tex]D=(-2)^2-4(5)(-3)\\D=64[/tex]

The discriminant obtained is greater than zero.

When [tex]D>0[/tex] the type of solution is: two distinct real roots.

kudzordzifrancis

ANSWER

The given trinomial will have two distinct real solutionss.

EXPLANATION

The given trinomial is

[tex]5 {x}^{2} - 2x - 3[/tex]

When we compare to

[tex] a{x}^{2} + bx + c[/tex]

, we have a=5, b=-2, c=-3

The discriminant of a quadratic trinomial helps us to predict the nature of the roots of a quadratic trinomial without necessarily solving for them.

We now use the discriminant

D=b²-4ac

to obtain,

[tex]D= {( - 2)}^{2} - 4(5)( - 3)[/tex]

[tex]D=4 + 60 = 64[/tex]

Since the discriminant is positive, the trinomial will have two distinct real solutions.

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