Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(3x^2+0=0\)
- \(-5x^2+717=-10x^2-3\)
- \(-4x^2-36=0\)
- \(6x^2+384=0\)
- \(4x^2-481=-2x^2+5\)
- \(-4x^2+36=0\)
- \(-7x^2-1183=0\)
- \(-5x^2-80=0\)
- \(-4x^2-503=-7x^2+4\)
- \(7x^2+0=0\)
- \(-6x^2+1176=0\)
- \(3(9x^2-9)=-(-26x^2-94)\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(3x^2+0=0 \\
\Leftrightarrow 3x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{3}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(-5x^2+717=-10x^2-3 \\ \Leftrightarrow -5x^2+10x^2=-3-717 \\
\Leftrightarrow 5x^2 = -720 \\
\Leftrightarrow x^2 = \frac{-720}{5} < 0 \\
V = \varnothing \\ -----------------\)
- \(-4x^2-36=0 \\
\Leftrightarrow -4x^2 = 36 \\
\Leftrightarrow x^2 = \frac{36}{-4} < 0 \\
V = \varnothing \\ -----------------\)
- \(6x^2+384=0 \\
\Leftrightarrow 6x^2 = -384 \\
\Leftrightarrow x^2 = \frac{-384}{6} < 0 \\
V = \varnothing \\ -----------------\)
- \(4x^2-481=-2x^2+5 \\ \Leftrightarrow 4x^2+2x^2=5+481 \\
\Leftrightarrow 6x^2 = 486 \\
\Leftrightarrow x^2 = \frac{486}{6}=81 \\
\Leftrightarrow x = 9 \vee x = -9 \\
V = \Big\{-9, 9 \Big\} \\ -----------------\)
- \(-4x^2+36=0 \\
\Leftrightarrow -4x^2 = -36 \\
\Leftrightarrow x^2 = \frac{-36}{-4}=9 \\
\Leftrightarrow x = 3 \vee x = -3 \\
V = \Big\{-3, 3 \Big\} \\ -----------------\)
- \(-7x^2-1183=0 \\
\Leftrightarrow -7x^2 = 1183 \\
\Leftrightarrow x^2 = \frac{1183}{-7} < 0 \\
V = \varnothing \\ -----------------\)
- \(-5x^2-80=0 \\
\Leftrightarrow -5x^2 = 80 \\
\Leftrightarrow x^2 = \frac{80}{-5} < 0 \\
V = \varnothing \\ -----------------\)
- \(-4x^2-503=-7x^2+4 \\ \Leftrightarrow -4x^2+7x^2=4+503 \\
\Leftrightarrow 3x^2 = 507 \\
\Leftrightarrow x^2 = \frac{507}{3}=169 \\
\Leftrightarrow x = 13 \vee x = -13 \\
V = \Big\{-13, 13 \Big\} \\ -----------------\)
- \(7x^2+0=0 \\
\Leftrightarrow 7x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{7}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(-6x^2+1176=0 \\
\Leftrightarrow -6x^2 = -1176 \\
\Leftrightarrow x^2 = \frac{-1176}{-6}=196 \\
\Leftrightarrow x = 14 \vee x = -14 \\
V = \Big\{-14, 14 \Big\} \\ -----------------\)
- \(3(9x^2-9)=-(-26x^2-94) \\ \Leftrightarrow 27x^2-27=26x^2+94 \\
\Leftrightarrow 27x^2-26x^2=94+27 \\
\Leftrightarrow x^2 = 121 \\
\Leftrightarrow x^2 = \frac{121}{1}=121 \\
\Leftrightarrow x = 11 \vee x = -11 \\
V = \Big\{-11, 11 \Big\} \\ -----------------\)