Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-2x^2-2=0\)
2. \(-7x^2-700=0\)
3. \(6x^2-864=0\)
4. \(-11x^2+188=-6x^2+8\)
5. \(-5(-9x^2+3)=-(-40x^2-5)\)
6. \(12x^2+1809=4x^2+9\)
7. \(x^2-109=-3x^2-9\)
8. \(3(-6x^2-3)=-(23x^2+14)\)
9. \(-x^2+212=-7x^2-4\)
10. \(4x^2-16=0\)
11. \(7x^2-343=0\)
12. \(-8x^2-512=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-2x^2-2=0 \\ \Leftrightarrow -2x^2 = 2 \\ \Leftrightarrow x^2 = \frac{2}{-2} < 0 \\ V = \varnothing \\ -----------------\)
2. \(-7x^2-700=0 \\ \Leftrightarrow -7x^2 = 700 \\ \Leftrightarrow x^2 = \frac{700}{-7} < 0 \\ V = \varnothing \\ -----------------\)
3. \(6x^2-864=0 \\ \Leftrightarrow 6x^2 = 864 \\ \Leftrightarrow x^2 = \frac{864}{6}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
4. \(-11x^2+188=-6x^2+8 \\ \Leftrightarrow -11x^2+6x^2=8-188 \\ \Leftrightarrow -5x^2 = -180 \\ \Leftrightarrow x^2 = \frac{-180}{-5}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
5. \(-5(-9x^2+3)=-(-40x^2-5) \\ \Leftrightarrow 45x^2-15=40x^2+5 \\ \Leftrightarrow 45x^2-40x^2=5+15 \\ \Leftrightarrow 5x^2 = 20 \\ \Leftrightarrow x^2 = \frac{20}{5}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
6. \(12x^2+1809=4x^2+9 \\ \Leftrightarrow 12x^2-4x^2=9-1809 \\ \Leftrightarrow 8x^2 = -1800 \\ \Leftrightarrow x^2 = \frac{-1800}{8} < 0 \\ V = \varnothing \\ -----------------\)
7. \(x^2-109=-3x^2-9 \\ \Leftrightarrow x^2+3x^2=-9+109 \\ \Leftrightarrow 4x^2 = 100 \\ \Leftrightarrow x^2 = \frac{100}{4}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
8. \(3(-6x^2-3)=-(23x^2+14) \\ \Leftrightarrow -18x^2-9=-23x^2-14 \\ \Leftrightarrow -18x^2+23x^2=-14+9 \\ \Leftrightarrow 5x^2 = -5 \\ \Leftrightarrow x^2 = \frac{-5}{5} < 0 \\ V = \varnothing \\ -----------------\)
9. \(-x^2+212=-7x^2-4 \\ \Leftrightarrow -x^2+7x^2=-4-212 \\ \Leftrightarrow 6x^2 = -216 \\ \Leftrightarrow x^2 = \frac{-216}{6} < 0 \\ V = \varnothing \\ -----------------\)
10. \(4x^2-16=0 \\ \Leftrightarrow 4x^2 = 16 \\ \Leftrightarrow x^2 = \frac{16}{4}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
11. \(7x^2-343=0 \\ \Leftrightarrow 7x^2 = 343 \\ \Leftrightarrow x^2 = \frac{343}{7}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
12. \(-8x^2-512=0 \\ \Leftrightarrow -8x^2 = 512 \\ \Leftrightarrow x^2 = \frac{512}{-8} < 0 \\ V = \varnothing \\ -----------------\)