The quadratic polynomial whose roots are 2 and 4 is

Correct option is A

The standard form of a quadratic polynomial is:

$$P(x) = x^2 - (\text{sum of roots})x + (\text{product of roots})$$​​


Step 1: Given roots are 2 and 4.
- Sum of roots:

Sum of roots = 2 + 4 = 6

- Product of roots:

Product of roots = 2 $$\times$$​ 4 = 8


Step 2: Substitute values into the formula:

P(x) = $$x^2 - (\text{sum of roots})x + (\text{product of roots})$$​​


P(x) = $$x^2 - 6x + 8$$​​


Step 3: Verify the options:
- Option A: $$x^2$$​ - 6x + 8 matches the derived polynomial.
- Option B: 2$$x^2$$​ - 3x + 8 is incorrect as it does not fit the sum and product of the roots.
- Option C: $$\frac{1}{2}x^2 - 6x + 8$$​ is incorrect as it changes the coefficients improperly.
- Option D: None of these is incorrect since Option A is correct.

Final Answer:
The quadratic polynomial is $$x^2$$​ - 6x + 8 . Correct Option: A.