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Given the following function: y=x^2+10x+25 Using your knowledge of discriminants, how many solutions does this function have?

Respuesta :

mhanifa

Answer:

  • One solution

Step-by-step explanation:

Given function:

  • y = x² + 10x + 25

This is a quadratic function.  

A quadratic equation has:

  • Two solutions if discriminant is positive;
  • One solution if discriminant is zero;
  • No solution if discriminant is negative

Find the discriminant of the given function:

  • D = b² - 4ac = 10² - 4*1*25 = 100 - 100 = 0

This function has one solution since its discriminant is zero.

semsee45

Answer:

one real solution

Step-by-step explanation:

Discriminant

[tex]b^2-4ac\quad\textsf{when}\:ax^2+bx+c=0[/tex]

[tex]\textsf{when }\:b^2-4ac > 0 \implies \textsf{two real solutions}[/tex]

[tex]\textsf{when }\:b^2-4ac=0 \implies \textsf{one real solution}[/tex]

[tex]\textsf{when }\:b^2-4ac < 0 \implies \textsf{no real solutions}[/tex]

Given function:

[tex]y=x^2+10x+25[/tex]

Therefore:

  • [tex]a = 1[/tex]
  • [tex]b = 10[/tex]
  • [tex]c = 25[/tex]

Substitute the given values into the discriminant:

[tex]\implies 10^2-4(1)(25)=0[/tex]

As the discriminant equals zero, there is one real solution.