Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(4(-6x^2-3x)=-(22x^2-x)\)
2. \(-4x^2-10x=-3x^2-3x\)
3. \(-4x^2-7x=0\)
4. \(-4(4x^2+10x)=-(15x^2+59x)\)
5. \(-5x^2+5x=0\)
6. \(-8x^2+25x=0\)
7. \(3(5x^2-8x)=-(-13x^2+x)\)
8. \(-6x^2-9x=-7x^2+7x\)
9. \(3x^2+25x=0\)
10. \(5(-4x^2-9x)=-(26x^2+50x)\)
11. \(4x^2-17x=0\)
12. \(3(4x^2+7x)=-(-17x^2-5x)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(4(-6x^2-3x)=-(22x^2-x) \\ \Leftrightarrow -24x^2-12x=-22x^2+x \\ \Leftrightarrow -24x^2-12x+22x^2-x= 0 \\ \Leftrightarrow -2x^2+13x=0 \\ \Leftrightarrow x(-2x+13) = 0 \\ \Leftrightarrow x = 0 \vee -2x+13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-13}{-2} = \frac{13}{2} \\ V = \Big\{ \frac{13}{2}; 0 \Big\} \\ -----------------\)
2. \(-4x^2-10x=-3x^2-3x \\ \Leftrightarrow -x^2-7x=0 \\ \Leftrightarrow x(-x-7) = 0 \\ \Leftrightarrow x = 0 \vee -x-7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{7}{-1} = -7 \\ V = \Big\{ 0 ; -7 \Big\} \\ -----------------\)
3. \(-4x^2-7x=0 \\ \Leftrightarrow x(-4x-7) = 0 \\ \Leftrightarrow x = 0 \vee -4x-7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{7}{-4} = \frac{-7}{4} \\ V = \Big\{ 0 ; \frac{-7}{4} \Big\} \\ -----------------\)
4. \(-4(4x^2+10x)=-(15x^2+59x) \\ \Leftrightarrow -16x^2-40x=-15x^2-59x \\ \Leftrightarrow -16x^2-40x+15x^2+59x= 0 \\ \Leftrightarrow -x^2-19x=0 \\ \Leftrightarrow x(-x-19) = 0 \\ \Leftrightarrow x = 0 \vee -x-19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{19}{-1} = -19 \\ V = \Big\{ 0 ; -19 \Big\} \\ -----------------\)
5. \(-5x^2+5x=0 \\ \Leftrightarrow x(-5x+5) = 0 \\ \Leftrightarrow x = 0 \vee -5x+5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-5}{-5} = 1 \\ V = \Big\{ 1; 0 \Big\} \\ -----------------\)
6. \(-8x^2+25x=0 \\ \Leftrightarrow x(-8x+25) = 0 \\ \Leftrightarrow x = 0 \vee -8x+25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-25}{-8} = \frac{25}{8} \\ V = \Big\{ \frac{25}{8}; 0 \Big\} \\ -----------------\)
7. \(3(5x^2-8x)=-(-13x^2+x) \\ \Leftrightarrow 15x^2-24x=13x^2-x \\ \Leftrightarrow 15x^2-24x-13x^2+x= 0 \\ \Leftrightarrow 2x^2+23x=0 \\ \Leftrightarrow x(2x+23) = 0 \\ \Leftrightarrow x = 0 \vee 2x+23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-23}{2} \\ V = \Big\{ 0 ; \frac{-23}{2} \Big\} \\ -----------------\)
8. \(-6x^2-9x=-7x^2+7x \\ \Leftrightarrow x^2-16x=0 \\ \Leftrightarrow x(x-16) = 0 \\ \Leftrightarrow x = 0 \vee x-16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{16}{1} = 16 \\ V = \Big\{ 16; 0 \Big\} \\ -----------------\)
9. \(3x^2+25x=0 \\ \Leftrightarrow x(3x+25) = 0 \\ \Leftrightarrow x = 0 \vee 3x+25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-25}{3} \\ V = \Big\{ 0 ; \frac{-25}{3} \Big\} \\ -----------------\)
10. \(5(-4x^2-9x)=-(26x^2+50x) \\ \Leftrightarrow -20x^2-45x=-26x^2-50x \\ \Leftrightarrow -20x^2-45x+26x^2+50x= 0 \\ \Leftrightarrow 6x^2-5x=0 \\ \Leftrightarrow x(6x-5) = 0 \\ \Leftrightarrow x = 0 \vee 6x-5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{5}{6} \\ V = \Big\{ \frac{5}{6}; 0 \Big\} \\ -----------------\)
11. \(4x^2-17x=0 \\ \Leftrightarrow x(4x-17) = 0 \\ \Leftrightarrow x = 0 \vee 4x-17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{17}{4} \\ V = \Big\{ \frac{17}{4}; 0 \Big\} \\ -----------------\)
12. \(3(4x^2+7x)=-(-17x^2-5x) \\ \Leftrightarrow 12x^2+21x=17x^2+5x \\ \Leftrightarrow 12x^2+21x-17x^2-5x= 0 \\ \Leftrightarrow -5x^2-16x=0 \\ \Leftrightarrow x(-5x-16) = 0 \\ \Leftrightarrow x = 0 \vee -5x-16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{16}{-5} = \frac{-16}{5} \\ V = \Big\{ 0 ; \frac{-16}{5} \Big\} \\ -----------------\)