Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(4x^2+2x=0\)
2. \(-11x^2+14x=-5x^2-2x\)
3. \(-4(4x^2+10x)=-(19x^2+51x)\)
4. \(4(3x^2+3x)=-(-13x^2-30x)\)
5. \(-x^2-26x=7x^2-5x\)
6. \(-x^2+16x=0\)
7. \(4x^2-31x=6x^2-9x\)
8. \(5x^2-21x=0\)
9. \(3(-7x^2+9x)=-(26x^2-14x)\)
10. \(4(4x^2-6x)=-(-17x^2+0x)\)
11. \(-x^2-8x=0\)
12. \(4(-6x^2+3x)=-(23x^2+13x)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(4x^2+2x=0 \\ \Leftrightarrow x(4x+2) = 0 \\ \Leftrightarrow x = 0 \vee 4x+2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-2}{4} = \frac{-1}{2} \\ V = \Big\{ 0 ; \frac{-1}{2} \Big\} \\ -----------------\)
2. \(-11x^2+14x=-5x^2-2x \\ \Leftrightarrow -6x^2+16x=0 \\ \Leftrightarrow x(-6x+16) = 0 \\ \Leftrightarrow x = 0 \vee -6x+16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-16}{-6} = \frac{8}{3} \\ V = \Big\{ \frac{8}{3}; 0 \Big\} \\ -----------------\)
3. \(-4(4x^2+10x)=-(19x^2+51x) \\ \Leftrightarrow -16x^2-40x=-19x^2-51x \\ \Leftrightarrow -16x^2-40x+19x^2+51x= 0 \\ \Leftrightarrow 3x^2-11x=0 \\ \Leftrightarrow x(3x-11) = 0 \\ \Leftrightarrow x = 0 \vee 3x-11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{11}{3} \\ V = \Big\{ \frac{11}{3}; 0 \Big\} \\ -----------------\)
4. \(4(3x^2+3x)=-(-13x^2-30x) \\ \Leftrightarrow 12x^2+12x=13x^2+30x \\ \Leftrightarrow 12x^2+12x-13x^2-30x= 0 \\ \Leftrightarrow -x^2+18x=0 \\ \Leftrightarrow x(-x+18) = 0 \\ \Leftrightarrow x = 0 \vee -x+18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-18}{-1} = 18 \\ V = \Big\{ 18; 0 \Big\} \\ -----------------\)
5. \(-x^2-26x=7x^2-5x \\ \Leftrightarrow -8x^2-21x=0 \\ \Leftrightarrow x(-8x-21) = 0 \\ \Leftrightarrow x = 0 \vee -8x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{-8} = \frac{-21}{8} \\ V = \Big\{ 0 ; \frac{-21}{8} \Big\} \\ -----------------\)
6. \(-x^2+16x=0 \\ \Leftrightarrow x(-x+16) = 0 \\ \Leftrightarrow x = 0 \vee -x+16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-16}{-1} = 16 \\ V = \Big\{ 16; 0 \Big\} \\ -----------------\)
7. \(4x^2-31x=6x^2-9x \\ \Leftrightarrow -2x^2-22x=0 \\ \Leftrightarrow x(-2x-22) = 0 \\ \Leftrightarrow x = 0 \vee -2x-22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{22}{-2} = -11 \\ V = \Big\{ 0 ; -11 \Big\} \\ -----------------\)
8. \(5x^2-21x=0 \\ \Leftrightarrow x(5x-21) = 0 \\ \Leftrightarrow x = 0 \vee 5x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{5} \\ V = \Big\{ \frac{21}{5}; 0 \Big\} \\ -----------------\)
9. \(3(-7x^2+9x)=-(26x^2-14x) \\ \Leftrightarrow -21x^2+27x=-26x^2+14x \\ \Leftrightarrow -21x^2+27x+26x^2-14x= 0 \\ \Leftrightarrow 5x^2-13x=0 \\ \Leftrightarrow x(5x-13) = 0 \\ \Leftrightarrow x = 0 \vee 5x-13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{13}{5} \\ V = \Big\{ \frac{13}{5}; 0 \Big\} \\ -----------------\)
10. \(4(4x^2-6x)=-(-17x^2+0x) \\ \Leftrightarrow 16x^2-24x=17x^2+0x \\ \Leftrightarrow 16x^2-24x-17x^2+0x= 0 \\ \Leftrightarrow -x^2+24x=0 \\ \Leftrightarrow x(-x+24) = 0 \\ \Leftrightarrow x = 0 \vee -x+24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-24}{-1} = 24 \\ V = \Big\{ 24; 0 \Big\} \\ -----------------\)
11. \(-x^2-8x=0 \\ \Leftrightarrow x(-x-8) = 0 \\ \Leftrightarrow x = 0 \vee -x-8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{8}{-1} = -8 \\ V = \Big\{ 0 ; -8 \Big\} \\ -----------------\)
12. \(4(-6x^2+3x)=-(23x^2+13x) \\ \Leftrightarrow -24x^2+12x=-23x^2-13x \\ \Leftrightarrow -24x^2+12x+23x^2+13x= 0 \\ \Leftrightarrow -x^2-25x=0 \\ \Leftrightarrow x(-x-25) = 0 \\ \Leftrightarrow x = 0 \vee -x-25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{25}{-1} = -25 \\ V = \Big\{ 0 ; -25 \Big\} \\ -----------------\)