Question

Question #121d0

Answer 1

`9`

Explanation:

The discriminant `Delta` of some quadratic expression `a x^(2) + b x + c` is in given by `b^(2) - 4 a c`.

Let's apply this to our quadratic expression `2 x^(2) - 7 x + 5`:

`Rightarrow Delta = (- 7)^(2) - 4 (2) (5)`

`Rightarrow Delta = 49 - 4 (10)`

`Rightarrow Delta = 49 - 40`

`therefore Delta = 9`

Therefore, the discriminant of the given quadratic expression is `9`.

Answer 2

See a solution process below:

Explanation:

The quadratic formula states:

For `ax^2 + bx + c = 0`, the values of `x` which are the solutions to the equation are given by:

`x = (-b +- sqrt(b^2 - 4ac))/(2a)`

The discriminate is the portion of the quadratic equation within the radical: `b^2 - 4ac`

If the discriminate is:
- Positive, you will get two real solutions
- Zero you get just ONE solution
- Negative you get complex solutions

To find the discriminant for this problem substitute:

`2` for `a`

`-7` for `b`

`5` for `c`

`-7^2 - (4 * 2 * 5) => 49 - 40 => 9`

Answer 3

The discriminant is 9.

Explanation:

The discriminant, d, for a quadratic expression of the form `ax^2+bx+c` is:

`d = b^2-4(a)(c)`

For the given expression, `2x^2-7x+5`, the discriminant is:

`d = (-7)^2-4(2)(5)`

`d = 49-40`

`d = 9`