Provide an appropriate response.
-For what values of a does the quadratic function $f ( x ) = a x ^ { 2 } + 4 x + 5$ have two $x$ -intercepts?

Question

Provide an appropriate response. -For what values of a does the quadratic function $f ( x ) = a x ^ { 2 } + 4 x + 5$ have two $x$-intercepts? A) $a > \frac { 4 } { 5 }$ B) $a > \frac { 16 } { 5 }$ C) $a < \frac { 4 } { 5 }$ D) $a < \frac { 16 } { 5 }$

Quizplus · Accepted Answer

For a quadratic function to have two x-intercepts, the discriminant must be positive. The discriminant of $ax^2 + 4x + 5$ is $16 - 20a$. Setting $16 - 20a > 0$ gives $a < \frac{4}{5}$.

Provide an Appropriate Response f(x)=ax2+4x+5f ( x ) = a x ^ { 2 } + 4 x + 5f(x)=ax2+4x+5

Provide an Appropriate Response $f ( x ) = a x ^ { 2 } + 4 x + 5$