A quadratic equation with integral coefficient has integral roots. Justify your answer.

Does there exist a quadratic equation whose coefficients are rational but both of its roots are irrational? Justify your answer.

Find the roots of the quadratic equations by using the quadratic formula in each of the following

$2x^2-3x-5=0$

Find the roots of the quadratic equation by using the quadratic formula in each of the following 

$5x^2+13x+8=0$

Find the roots of the quadratic equations by using the quadratic formula in each of the following 

$-3{\mathrm{x}}^2+5\mathrm{x}+12=0$

Find the roots of the quadratic equations by using the quadratic formula in each of the following 

$-x^2+7x-10=0$