Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-2x^2+0=0\)
2. \(3x^2-12=0\)
3. \(x^2+31=-3x^2-5\)
4. \(8x^2-1352=0\)
5. \(-5x^2-605=0\)
6. \(-8x^2+47=-3x^2+2\)
7. \(4(-6x^2+3)=-(16x^2+276)\)
8. \(7x^2-1372=0\)
9. \(-6x^2-294=0\)
10. \(-2(-6x^2-3)=-(-10x^2-24)\)
11. \(-3x^2-729=2x^2-9\)
12. \(4x^2+0=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-2x^2+0=0 \\ \Leftrightarrow -2x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-2}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
2. \(3x^2-12=0 \\ \Leftrightarrow 3x^2 = 12 \\ \Leftrightarrow x^2 = \frac{12}{3}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
3. \(x^2+31=-3x^2-5 \\ \Leftrightarrow x^2+3x^2=-5-31 \\ \Leftrightarrow 4x^2 = -36 \\ \Leftrightarrow x^2 = \frac{-36}{4} < 0 \\ V = \varnothing \\ -----------------\)
4. \(8x^2-1352=0 \\ \Leftrightarrow 8x^2 = 1352 \\ \Leftrightarrow x^2 = \frac{1352}{8}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
5. \(-5x^2-605=0 \\ \Leftrightarrow -5x^2 = 605 \\ \Leftrightarrow x^2 = \frac{605}{-5} < 0 \\ V = \varnothing \\ -----------------\)
6. \(-8x^2+47=-3x^2+2 \\ \Leftrightarrow -8x^2+3x^2=2-47 \\ \Leftrightarrow -5x^2 = -45 \\ \Leftrightarrow x^2 = \frac{-45}{-5}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
7. \(4(-6x^2+3)=-(16x^2+276) \\ \Leftrightarrow -24x^2+12=-16x^2-276 \\ \Leftrightarrow -24x^2+16x^2=-276-12 \\ \Leftrightarrow -8x^2 = -288 \\ \Leftrightarrow x^2 = \frac{-288}{-8}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
8. \(7x^2-1372=0 \\ \Leftrightarrow 7x^2 = 1372 \\ \Leftrightarrow x^2 = \frac{1372}{7}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
9. \(-6x^2-294=0 \\ \Leftrightarrow -6x^2 = 294 \\ \Leftrightarrow x^2 = \frac{294}{-6} < 0 \\ V = \varnothing \\ -----------------\)
10. \(-2(-6x^2-3)=-(-10x^2-24) \\ \Leftrightarrow 12x^2+6=10x^2+24 \\ \Leftrightarrow 12x^2-10x^2=24-6 \\ \Leftrightarrow 2x^2 = 18 \\ \Leftrightarrow x^2 = \frac{18}{2}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
11. \(-3x^2-729=2x^2-9 \\ \Leftrightarrow -3x^2-2x^2=-9+729 \\ \Leftrightarrow -5x^2 = 720 \\ \Leftrightarrow x^2 = \frac{720}{-5} < 0 \\ V = \varnothing \\ -----------------\)
12. \(4x^2+0=0 \\ \Leftrightarrow 4x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{4}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)