Question

The number of real solutions to the quadratic equ 5a² + 30a + 45 = 0

Answer 1

Answer:

two equal, real solutions

Step-by-step explanation:

The quickest way to determine this is to find the discriminant b^2 - 4ac.  If this determinant (D) is > 0, the quadratic has two different real roots; if + 0, the quadratic has two equal real roots, and if < 0, the quadratic has two imaginary or complex roots.

Here a = 5, b = 30 and c = 45.  The discriminant is

30^2 - 4(5)(45)  =  900 - 900 = 0

and so this quadratic has two equal, real solutions.

Answer 2

The answer is 1.

There is one unique real solution, which is x = -3.

Hello, please consider the following.

$5a^2+30a+45 = 0\\\\ 5(a^2+6a+9)=0\\\\ a^2+6a+9=0\\\\ a^2+2*3*a+3^2=(a+3)^2=0\\\\\boxed{a=-3}$

Thank you