A quadratic equation whose roots are$$\frac{5}{3}$$​ and -$$\frac{3}{4}$$​ is:

Correct option is A

Given:

Given roots of equation =$$\frac{5}{3}$$​ and $$-\frac{3}{4}$$​​

Formula Used:

If $$\alpha$$​ and $$\beta$$​ are roots of a equation:

Then equation is given by $$: x^2 - (\alpha + \beta)x + (\alpha\beta) = 0$$​​

Solution:

Here we have roots of equation  $$\alpha = \frac{5}{3}$$​ and $$\beta -\frac{3}{4}$$​​

Then $$x^2 -\left(\frac{5}{3} -\frac{3}{4}\right)x + \left(\frac{5}{3}\right)\left(-\frac{3}{4}\right)=0$$​

​$$x^2 -\left(\frac{20-9}{12} \right)x - \left(\frac{5}{4}\right)=0$$​​

​$$x^2 -\left(\frac{11}{12} \right)x - \left(\frac{5}{4}\right)=0$$​​

​$$\left(\frac{12x^2 -11x-15}{12} \right)x =0$$​​

​$$12x^2 -11x-15=0$$​​