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f(x)=6x^2+10x-1

What is the value of the discriminant of f?

How many distinct real number zeros does f have?

Respuesta :

calculista

Answer:

Two different real solutions

Step-by-step explanation:

we know that

In a quadratic equation of the form

[tex]ax^{2} +bx+c=0[/tex]

The discriminant D is equal to

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

Equate f(x) to zero

so

[tex]6x^{2} +10x-1=0[/tex]  

we have

[tex]a=6\\b=10\\c=-1[/tex]

substitute

[tex]D=10^2-4(6)(-1)[/tex]

[tex]D=100+24[/tex]

[tex]D=124[/tex]

The value of D is greater than zero

That means ----> The quadratic equation has two different real solutions

Value of discriminant is [tex]124[/tex]

Also, the polynomial has two distinct real number zeros.

Discriminant

  • A polynomial's discriminant is a number that depends on the coefficients and defines several properties of the roots.
  • For a polynomial of the form [tex]\boldsymbol{f(x)=ax^2+bx+c}[/tex], discriminant is given by [tex]\boldsymbol{b^2-4ac}[/tex]. If [tex]b^2-4ac>0[/tex] then the polynomial has two distinct real number zeros.

Consider the polynomial [tex]f(x)=6x^2+10x-1[/tex]

Discriminant [tex]=10^{2}-4(6)(-1)[/tex]

                     [tex]=100+24\\=\boldsymbol{124}[/tex]

Here, value of discriminant is greater than [tex]0[/tex]

So, the polynomial has two distinct real number zeros

Find out more information about discriminant here:

https://brainly.com/question/15884086?referrer=searchResults

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