Question

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

Answer 1

one real solution

Explanation:

Discriminant

`b^2-4ac\quad\textsf{when}\:ax^2+bx+c=0`

`\textsf{when }\:b^2-4ac > 0 \implies \textsf{two real solutions}`

`\textsf{when }\:b^2-4ac=0 \implies \textsf{one real solution}`

`\textsf{when }\:b^2-4ac < 0 \implies \textsf{no real solutions}`

Given function:

`y=x^2+10x+25`

Therefore:

• 
  `a = 1`
• 
  `b = 10`
• 
  `c = 25`

Substitute the given values into the discriminant:

`\implies 10^2-4(1)(25)=0`

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

Answer 2

• One solution

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.