Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(4x^2+0=0\)
2. \(3x^2-7=8x^2-7\)
3. \(6x^2+864=0\)
4. \(-2(-4x^2-5)=-(-11x^2-310)\)
5. \(-x^2-399=4x^2+6\)
6. \(3(-9x^2+3)=-(35x^2-9)\)
7. \(-4(-10x^2-7)=-(-38x^2+364)\)
8. \(2(-6x^2-5)=-(4x^2+10)\)
9. \(-2(-9x^2+10)=-(-13x^2+0)\)
10. \(8x^2-128=0\)
11. \(-5x^2+1125=0\)
12. \(8x^2-8=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(4x^2+0=0 \\ \Leftrightarrow 4x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{4}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
2. \(3x^2-7=8x^2-7 \\ \Leftrightarrow 3x^2-8x^2=-7+7 \\ \Leftrightarrow -5x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-5}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
3. \(6x^2+864=0 \\ \Leftrightarrow 6x^2 = -864 \\ \Leftrightarrow x^2 = \frac{-864}{6} < 0 \\ V = \varnothing \\ -----------------\)
4. \(-2(-4x^2-5)=-(-11x^2-310) \\ \Leftrightarrow 8x^2+10=11x^2+310 \\ \Leftrightarrow 8x^2-11x^2=310-10 \\ \Leftrightarrow -3x^2 = 300 \\ \Leftrightarrow x^2 = \frac{300}{-3} < 0 \\ V = \varnothing \\ -----------------\)
5. \(-x^2-399=4x^2+6 \\ \Leftrightarrow -x^2-4x^2=6+399 \\ \Leftrightarrow -5x^2 = 405 \\ \Leftrightarrow x^2 = \frac{405}{-5} < 0 \\ V = \varnothing \\ -----------------\)
6. \(3(-9x^2+3)=-(35x^2-9) \\ \Leftrightarrow -27x^2+9=-35x^2+9 \\ \Leftrightarrow -27x^2+35x^2=9-9 \\ \Leftrightarrow 8x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{8}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
7. \(-4(-10x^2-7)=-(-38x^2+364) \\ \Leftrightarrow 40x^2+28=38x^2-364 \\ \Leftrightarrow 40x^2-38x^2=-364-28 \\ \Leftrightarrow 2x^2 = -392 \\ \Leftrightarrow x^2 = \frac{-392}{2} < 0 \\ V = \varnothing \\ -----------------\)
8. \(2(-6x^2-5)=-(4x^2+10) \\ \Leftrightarrow -12x^2-10=-4x^2-10 \\ \Leftrightarrow -12x^2+4x^2=-10+10 \\ \Leftrightarrow -8x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-8}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
9. \(-2(-9x^2+10)=-(-13x^2+0) \\ \Leftrightarrow 18x^2-20=13x^2+0 \\ \Leftrightarrow 18x^2-13x^2=0+20 \\ \Leftrightarrow 5x^2 = 20 \\ \Leftrightarrow x^2 = \frac{20}{5}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
10. \(8x^2-128=0 \\ \Leftrightarrow 8x^2 = 128 \\ \Leftrightarrow x^2 = \frac{128}{8}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
11. \(-5x^2+1125=0 \\ \Leftrightarrow -5x^2 = -1125 \\ \Leftrightarrow x^2 = \frac{-1125}{-5}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
12. \(8x^2-8=0 \\ \Leftrightarrow 8x^2 = 8 \\ \Leftrightarrow x^2 = \frac{8}{8}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)