Question

Help please, I attached the question. Is it a!? 

Answer 1

The answer to this is A

Answer 2

Answer:

A

Step-by-step explanation:

Recall that for a quadratic equation of the form:

$0=ax^2+bx+c$

The number of solutions it has can be determined using its discriminant:  

$\Delta = b^2-4ac$

Where:

• If the discriminant is positive, we have two real solutions.
• If the discriminant is negative, we have no real solutions.
• And if the discriminant is zero, we have exactly one solution.

We have the equation:

$2x^2+5x-k=0$

Thus, a = 2, b = 5, and c = -k.

In order for the equation to have exactly one distinct solution, the discriminant must equal zero. Hence:

$b^2-4ac=0$

Substitute:

$(5)^2-4(2)(-k)=0$

Solve for k. Simplify:

$25+8k=0$

Solve:

$\displaystyle k = -\frac{25}{8}$

Thus, our answer is indeed A.