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, its discriminant $b^2 - 4ac$ must be greater than 0. Here, $a = a$, $b = 4$, and $c = 5$. Thus, the discriminant is $4^2 - 4 \cdot a \cdot 5 = 16 - 20a$. For this to be greater than 0, $16 - 20a > 0$, which simplifies to $a < \frac{4}{5}$.

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

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