Question

find a quadratic equation in X having 5/2 and 2/5 are its roots​

Answer 1

given roots are 5 /2 ,2 and 2/ 5

now,

sum of roots = 29/10

product of roots = 1

so required quadratic equation is

x^2-29/10x +1 =0

10x^2-29x +10 = 0

hope it works ❤️｡◕‿◕｡

plz mark it as brainliest answer (✷‿✷)

Answer 2

The quadratic equation is 10x - 29x + 10.

Step-by-step explanation:

The roots of the quadratic equation are:

$\alpha =\frac{5}{2}\, \ and \, \beta =\frac{2}{5}$

Then the factors of the equation are:

$(x-\frac{5}{2})(x-\frac{2}{5})$

Determine the equation as follows:

$(x-\frac{5}{2})(x-\frac{2}{5})=0$

$x(x-\frac{2}{5})-\frac{5}{2}(x-\frac{2}{5})=0$

$x^{2}-\frac{2}{5}x-\frac{5}{2}x+1=0$

$\frac{10x^{2}-4x-25x+10}{10}=0$

$10x^{2}-29x+10=0$

Thus, the quadratic equation is 10x - 29x + 10.