In copying a quadratic equation of the form, the coefficient of x was wrongly written as $-10$ in place of $-11$ and the roots were found to be 4 and 6. If $\alpha ,\beta$   are the roots of the correct equation, then the value of ${\alpha }^4+{\beta }^4$   must be equal to.

Correct equation is   $x^2-11x+q=0$ 

Incorrect equation is  $x^2-10x+q=0$
Given roots of Eq. (ii) are 4 and 6    Product of roots of the incorrect equations is 

Ie,  $q=4\times 6=24$   From Eq. (i), correct equation is   $x^2-11x+24=0$

x=3,8
 Ie,  $\alpha =3,\beta =8$    $\therefore {\alpha }^4+{\beta }^4=3^4+8^4=81+4096$     =4177