The quadratic equation \(\displaystyle{y}={a}{x}^{{2}}+{b}{x}+{c}\) has roots

daurialebraslmc

daurialebraslmc

Answered question

2022-04-11

The quadratic equation y=ax2+bx+c has roots x=α and x=β. Find an equation that has roots x=α2 and x=β2.

Answer & Explanation

Coupewopmergorlpt

Coupewopmergorlpt

Beginner2022-04-12Added 13 answers

Apply the Graeffe root-squaring method.
ax2+bx+c=0
ax2+c=bx separating even and odd degree terms
a2x4+2acx2+c2=b2x2 after squaring
a2(x2)2+(2acb2)(x2)+c2=0.

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