Question

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


Answer 1

the answer to this is A

Answer 2

A

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 = -(25)/(8)`

Thus, our answer is indeed A.