If sum and product of the roots of a quadratic equation are $$(4-3\sqrt{2})$$ and –28, respectively, then find the quadratic equation.​

Correct option is D

Given:

Sum of roots = 4 -$$3\sqrt{2}$$​​

Product of roots = -28

Formula Used:

For quadratic with roots $$(\alpha,\beta): x^2 - (\alpha+\beta)x + \alpha\beta = 0$$​ (Vieta’s formulas)

Solution:

​$$\alpha+\beta = 4 - 3\sqrt{2}, \alpha\beta = -28$$​​

Quadratic:
​$$x^2 - (4 - 3\sqrt{2})x - 28 = 0.$$​​