Co-aontaran ailseabrachSgilean ailseabrach

Bidh sinn a' fuasgladh abairtean ioma-theirmeach le ailseabra gus na freumhan a dhearbhadh - far am bi lùb a' gearradh an \(x\)-axis.

Tha freumh fuincsean ioma-theirmeach, \(f(x)\), na luach airson \(x\) far a bheil \(f(x) = 0\).

• Fuasgail \(f(x) = 0\)
• Lorg na freumhan aig \(f(x)\)
• Lorg far a bheil \(f(x)\) a' gearradh an \(x\)-axis

Lorg na freumhan aig \({x^3} + 4{x^2} + x - 6 = 0\)

\(f(1) = {(1)^3} + 4{(1)^2} + (1) - 6 = 0\)

Mar sin 's e factar a th' ann an \((x - 1)\).

\((x - 1)({x^2} + 5x + 6) = 0\)

\((x - 1)(x + 3)(x + 2) = 0\)

\(x - 1 = 0\,mar\,sin\,x = 1\)

\(x + 3 = 0\,mar\,sin\,x = - 3\)

\(x + 2 = 0\,mar\,sin\,x = - 2\)

Mar sin tha na freumhan ann nuair a tha \(x\) = -3, -2 agus 1.

Fuasgail: \(2{x^4} + 9{x^3} - 18{x^2} - 71x - 30 = 0\)

\(f(1) = 2{(1)^4} + 9{(1)^3} - 18{(1)^2} - 71(1) - 30 = - 108\)

\(f( - 1) = 2{( - 1)^4} + 9{( - 1)^3} - 18{( - 1)^2} - 71( - 1) - 30 = 46\)

\(f(2) = 2{(2)^4} + 9{(2)^3} - 18{(2)^2} - 71(2) - 30 = - 140\)

\(f( - 2) = 2{( - 2)^4} + 9{( - 2)^3} - 18{( - 2)^2} - 71( - 2) - 30 = 0\)

Mar sin 's e factar a th' ann an \((x + 2)\).

\((x + 2)(2{x^3} + 5{x^2} - 28x - 15) = 0\)

\(f(3) = 2{(3)^3} + 5{(3)^2} - 28(3) - 15 = 0\)

Mar sin 's e factar a th' ann an \((x - 3)\).

\((x + 2)(x - 3)(2{x^2} + 11x + 5) = 0\)

\((x + 2)(x - 3)(x + 5)(2x + 1) = 0\)

\(x + 2 = 0\,mar\,sin\,x = - 2\)

\(x - 3 = 0\,mar\,sin\,x = 3\)

\(x + 5 = 0\,mar\,sin\,x = - 5\)

\(2x + 1 = 0\,mar\,sin\,x = - \frac{1}{2}\)