Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(4(7x^2-2x)=-(-23x^2+4x)\)
2. \(-15x^2+7x=-7x^2-10x\)
3. \(-2(3x^2-9x)=-(10x^2+3x)\)
4. \(7x^2-12x=0\)
5. \(3x^2+23x=-4x^2+9x\)
6. \(3x^2-17x=0\)
7. \(-2(-2x^2+8x)=-(4x^2-8x)\)
8. \(-6x^2-x=-4x^2+2x\)
9. \(13x^2+22x=10x^2+5x\)
10. \(-4(2x^2+10x)=-(4x^2+24x)\)
11. \(-5x^2-20x=0\)
12. \(-3x^2-16x=3x^2-9x\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(4(7x^2-2x)=-(-23x^2+4x) \\ \Leftrightarrow 28x^2-8x=23x^2-4x \\ \Leftrightarrow 28x^2-8x-23x^2+4x= 0 \\ \Leftrightarrow 5x^2+4x=0 \\ \Leftrightarrow x(5x+4) = 0 \\ \Leftrightarrow x = 0 \vee 5x+4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-4}{5} \\ V = \Big\{ 0 ; \frac{-4}{5} \Big\} \\ -----------------\)
2. \(-15x^2+7x=-7x^2-10x \\ \Leftrightarrow -8x^2+17x=0 \\ \Leftrightarrow x(-8x+17) = 0 \\ \Leftrightarrow x = 0 \vee -8x+17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-17}{-8} = \frac{17}{8} \\ V = \Big\{ \frac{17}{8}; 0 \Big\} \\ -----------------\)
3. \(-2(3x^2-9x)=-(10x^2+3x) \\ \Leftrightarrow -6x^2+18x=-10x^2-3x \\ \Leftrightarrow -6x^2+18x+10x^2+3x= 0 \\ \Leftrightarrow 4x^2-21x=0 \\ \Leftrightarrow x(4x-21) = 0 \\ \Leftrightarrow x = 0 \vee 4x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{4} \\ V = \Big\{ \frac{21}{4}; 0 \Big\} \\ -----------------\)
4. \(7x^2-12x=0 \\ \Leftrightarrow x(7x-12) = 0 \\ \Leftrightarrow x = 0 \vee 7x-12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{12}{7} \\ V = \Big\{ \frac{12}{7}; 0 \Big\} \\ -----------------\)
5. \(3x^2+23x=-4x^2+9x \\ \Leftrightarrow 7x^2+14x=0 \\ \Leftrightarrow x(7x+14) = 0 \\ \Leftrightarrow x = 0 \vee 7x+14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-14}{7} = -2 \\ V = \Big\{ 0 ; -2 \Big\} \\ -----------------\)
6. \(3x^2-17x=0 \\ \Leftrightarrow x(3x-17) = 0 \\ \Leftrightarrow x = 0 \vee 3x-17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{17}{3} \\ V = \Big\{ \frac{17}{3}; 0 \Big\} \\ -----------------\)
7. \(-2(-2x^2+8x)=-(4x^2-8x) \\ \Leftrightarrow 4x^2-16x=-4x^2+8x \\ \Leftrightarrow 4x^2-16x+4x^2-8x= 0 \\ \Leftrightarrow 8x^2+24x=0 \\ \Leftrightarrow x(8x+24) = 0 \\ \Leftrightarrow x = 0 \vee 8x+24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-24}{8} = -3 \\ V = \Big\{ 0 ; -3 \Big\} \\ -----------------\)
8. \(-6x^2-x=-4x^2+2x \\ \Leftrightarrow -2x^2-3x=0 \\ \Leftrightarrow x(-2x-3) = 0 \\ \Leftrightarrow x = 0 \vee -2x-3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{3}{-2} = \frac{-3}{2} \\ V = \Big\{ 0 ; \frac{-3}{2} \Big\} \\ -----------------\)
9. \(13x^2+22x=10x^2+5x \\ \Leftrightarrow 3x^2+17x=0 \\ \Leftrightarrow x(3x+17) = 0 \\ \Leftrightarrow x = 0 \vee 3x+17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-17}{3} \\ V = \Big\{ 0 ; \frac{-17}{3} \Big\} \\ -----------------\)
10. \(-4(2x^2+10x)=-(4x^2+24x) \\ \Leftrightarrow -8x^2-40x=-4x^2-24x \\ \Leftrightarrow -8x^2-40x+4x^2+24x= 0 \\ \Leftrightarrow -4x^2+16x=0 \\ \Leftrightarrow x(-4x+16) = 0 \\ \Leftrightarrow x = 0 \vee -4x+16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-16}{-4} = 4 \\ V = \Big\{ 4; 0 \Big\} \\ -----------------\)
11. \(-5x^2-20x=0 \\ \Leftrightarrow x(-5x-20) = 0 \\ \Leftrightarrow x = 0 \vee -5x-20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{20}{-5} = -4 \\ V = \Big\{ 0 ; -4 \Big\} \\ -----------------\)
12. \(-3x^2-16x=3x^2-9x \\ \Leftrightarrow -6x^2-7x=0 \\ \Leftrightarrow x(-6x-7) = 0 \\ \Leftrightarrow x = 0 \vee -6x-7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{7}{-6} = \frac{-7}{6} \\ V = \Big\{ 0 ; \frac{-7}{6} \Big\} \\ -----------------\)