If \(\alpha\) and \(\beta\) are the roots of the equation \[2x^2+3x+2 = 0,\] find the equation whose roots are \(\alpha+1\) and \(\beta+1\).

Can we solve this problem without computing \(\alpha\) and \(\beta\) explicitly?

Can we solve this problem without computing \(\alpha\) and \(\beta\) explicitly?