Question

Does the quadratic function

Answer 1

Answer:

No real zeros.

Step-by-step 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.

Answer 2

5x^2 + 5x + 21 = 0

No real solution

no x - intercept