Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-3x^2+300=0\)
2. \(8x^2+288=0\)
3. \(3(6x^2-7)=-(-15x^2+9)\)
4. \(6x^2-384=0\)
5. \(2(-6x^2-2)=-(10x^2-238)\)
6. \(6x^2-6=0\)
7. \(6x^2-203=8x^2-3\)
8. \(2x^2+0=0\)
9. \(-5(-8x^2+5)=-(-38x^2+17)\)
10. \(-6x^2+0=0\)
11. \(-3x^2+136=-7x^2-8\)
12. \(3x^2-75=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-3x^2+300=0 \\ \Leftrightarrow -3x^2 = -300 \\ \Leftrightarrow x^2 = \frac{-300}{-3}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
2. \(8x^2+288=0 \\ \Leftrightarrow 8x^2 = -288 \\ \Leftrightarrow x^2 = \frac{-288}{8} < 0 \\ V = \varnothing \\ -----------------\)
3. \(3(6x^2-7)=-(-15x^2+9) \\ \Leftrightarrow 18x^2-21=15x^2-9 \\ \Leftrightarrow 18x^2-15x^2=-9+21 \\ \Leftrightarrow 3x^2 = 12 \\ \Leftrightarrow x^2 = \frac{12}{3}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
4. \(6x^2-384=0 \\ \Leftrightarrow 6x^2 = 384 \\ \Leftrightarrow x^2 = \frac{384}{6}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
5. \(2(-6x^2-2)=-(10x^2-238) \\ \Leftrightarrow -12x^2-4=-10x^2+238 \\ \Leftrightarrow -12x^2+10x^2=238+4 \\ \Leftrightarrow -2x^2 = 242 \\ \Leftrightarrow x^2 = \frac{242}{-2} < 0 \\ V = \varnothing \\ -----------------\)
6. \(6x^2-6=0 \\ \Leftrightarrow 6x^2 = 6 \\ \Leftrightarrow x^2 = \frac{6}{6}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
7. \(6x^2-203=8x^2-3 \\ \Leftrightarrow 6x^2-8x^2=-3+203 \\ \Leftrightarrow -2x^2 = 200 \\ \Leftrightarrow x^2 = \frac{200}{-2} < 0 \\ V = \varnothing \\ -----------------\)
8. \(2x^2+0=0 \\ \Leftrightarrow 2x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{2}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
9. \(-5(-8x^2+5)=-(-38x^2+17) \\ \Leftrightarrow 40x^2-25=38x^2-17 \\ \Leftrightarrow 40x^2-38x^2=-17+25 \\ \Leftrightarrow 2x^2 = 8 \\ \Leftrightarrow x^2 = \frac{8}{2}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
10. \(-6x^2+0=0 \\ \Leftrightarrow -6x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-6}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
11. \(-3x^2+136=-7x^2-8 \\ \Leftrightarrow -3x^2+7x^2=-8-136 \\ \Leftrightarrow 4x^2 = -144 \\ \Leftrightarrow x^2 = \frac{-144}{4} < 0 \\ V = \varnothing \\ -----------------\)
12. \(3x^2-75=0 \\ \Leftrightarrow 3x^2 = 75 \\ \Leftrightarrow x^2 = \frac{75}{3}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)