If α,β are the roots of the equation 3x2+5x+4=0, then the quadratic equation whose roots are α2,β2.
9x2−x+16=0
α+β=−53, αβ=43
To find the equation whose roots are α2,β2, we have to find α2+β2 and α2β2
α2+β2=(α+β)2−2αβ =259−2×43 =19α2β2=169
The equation is :
x2−19x+169=0
⇒9x2−x+16=0