Question

Does the quadratic function

f(x) = 5x² + 5x + 21 have one,
two, or no real zeros? Utilize the
quadratic formula to determine
the answer.

Answer 1

5x^2 + 5x + 21 = 0

No real solution

no x - intercept

Answer 2

No real zeros.

Explanation:

`\boxed{\begin{minipage}{7.4 cm}\underline{Discriminant of the Quadratic Formula}\\\\$b^2-4ac$ \quad when $ax^2+bx+c=0$\\\\When $b^2-4ac > 0 \implies$ two real zeros.\\When $b^2-4ac=0 \implies$ one real zero.\\When $b^2-4ac < 0 \implies$ no real zeros.\\\end{minipage}}`

The value of the discriminant shows how many zeros the function has.

Given quadratic function:

`f(x)=5x^2+5x+21`

Therefore:

• a = 5
• b = 5
• c = 21

Substitute the values into the discriminant and solve:

`\begin{aligned}\implies b^2-4ac&=(5)^2-4(5)(21)\\& = 25 - 20(21)\\&=25-420\\&=-395\end{aligned}`

Therefore, as -395 < 0, there are no real zeros.