Question

Please write a lot and explain this solution please

Answer 1

Fourth option

Explanation:

The discriminant of a quadratic in the form of

`y = ax {}^(2) + bx + c`

is

`{b}^(2) - 4ac`

Here , b is -6, a is 1, and c is 9

So we get

`{6}^(2) - 4(1)(9) = 36 - 36 = 0`

So the discriminant is 0.

Since we have a discriminant of 0, this means our x intercept lie at the vertex thus we only have 1 real solution.

If we had a positive discriminant, that means we have two x intercepts(two rational roots)

Why? Because in the quadratic formula, notice that plus minus symbol. It means we have two possible x intercepts.

If we had a negative discriminant, we will have 2 imaginary roots

Why? Because not only we have a plus or minus symbol, you will learn that the square root of a negative number is an imaginary, complex number.

So the answer is D.