Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(5(8x^2+10x)=-(-38x^2-71x)\)
2. \(4(10x^2+4x)=-(-41x^2+0x)\)
3. \(-14x^2+13x=-9x^2-2x\)
4. \(2(5x^2-6x)=-(-11x^2+10x)\)
5. \(-14x^2-7x=-6x^2-4x\)
6. \(4x^2-7x=0\)
7. \(6x^2+13x=0\)
8. \(2(2x^2+5x)=-(-8x^2-4x)\)
9. \(5x^2-16x=8x^2-6x\)
10. \(8x^2-20x=0\)
11. \(-x^2-9x=-6x^2+10x\)
12. \(5(-4x^2-10x)=-(18x^2+50x)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(5(8x^2+10x)=-(-38x^2-71x) \\ \Leftrightarrow 40x^2+50x=38x^2+71x \\ \Leftrightarrow 40x^2+50x-38x^2-71x= 0 \\ \Leftrightarrow 2x^2+21x=0 \\ \Leftrightarrow x(2x+21) = 0 \\ \Leftrightarrow x = 0 \vee 2x+21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-21}{2} \\ V = \Big\{ 0 ; \frac{-21}{2} \Big\} \\ -----------------\)
2. \(4(10x^2+4x)=-(-41x^2+0x) \\ \Leftrightarrow 40x^2+16x=41x^2+0x \\ \Leftrightarrow 40x^2+16x-41x^2+0x= 0 \\ \Leftrightarrow -x^2-16x=0 \\ \Leftrightarrow x(-x-16) = 0 \\ \Leftrightarrow x = 0 \vee -x-16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{16}{-1} = -16 \\ V = \Big\{ 0 ; -16 \Big\} \\ -----------------\)
3. \(-14x^2+13x=-9x^2-2x \\ \Leftrightarrow -5x^2+15x=0 \\ \Leftrightarrow x(-5x+15) = 0 \\ \Leftrightarrow x = 0 \vee -5x+15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-15}{-5} = 3 \\ V = \Big\{ 3; 0 \Big\} \\ -----------------\)
4. \(2(5x^2-6x)=-(-11x^2+10x) \\ \Leftrightarrow 10x^2-12x=11x^2-10x \\ \Leftrightarrow 10x^2-12x-11x^2+10x= 0 \\ \Leftrightarrow -x^2+2x=0 \\ \Leftrightarrow x(-x+2) = 0 \\ \Leftrightarrow x = 0 \vee -x+2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-2}{-1} = 2 \\ V = \Big\{ 2; 0 \Big\} \\ -----------------\)
5. \(-14x^2-7x=-6x^2-4x \\ \Leftrightarrow -8x^2-3x=0 \\ \Leftrightarrow x(-8x-3) = 0 \\ \Leftrightarrow x = 0 \vee -8x-3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{3}{-8} = \frac{-3}{8} \\ V = \Big\{ 0 ; \frac{-3}{8} \Big\} \\ -----------------\)
6. \(4x^2-7x=0 \\ \Leftrightarrow x(4x-7) = 0 \\ \Leftrightarrow x = 0 \vee 4x-7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{7}{4} \\ V = \Big\{ \frac{7}{4}; 0 \Big\} \\ -----------------\)
7. \(6x^2+13x=0 \\ \Leftrightarrow x(6x+13) = 0 \\ \Leftrightarrow x = 0 \vee 6x+13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-13}{6} \\ V = \Big\{ 0 ; \frac{-13}{6} \Big\} \\ -----------------\)
8. \(2(2x^2+5x)=-(-8x^2-4x) \\ \Leftrightarrow 4x^2+10x=8x^2+4x \\ \Leftrightarrow 4x^2+10x-8x^2-4x= 0 \\ \Leftrightarrow -4x^2-6x=0 \\ \Leftrightarrow x(-4x-6) = 0 \\ \Leftrightarrow x = 0 \vee -4x-6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{6}{-4} = \frac{-3}{2} \\ V = \Big\{ 0 ; \frac{-3}{2} \Big\} \\ -----------------\)
9. \(5x^2-16x=8x^2-6x \\ \Leftrightarrow -3x^2-10x=0 \\ \Leftrightarrow x(-3x-10) = 0 \\ \Leftrightarrow x = 0 \vee -3x-10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{10}{-3} = \frac{-10}{3} \\ V = \Big\{ 0 ; \frac{-10}{3} \Big\} \\ -----------------\)
10. \(8x^2-20x=0 \\ \Leftrightarrow x(8x-20) = 0 \\ \Leftrightarrow x = 0 \vee 8x-20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{20}{8} = \frac{5}{2} \\ V = \Big\{ \frac{5}{2}; 0 \Big\} \\ -----------------\)
11. \(-x^2-9x=-6x^2+10x \\ \Leftrightarrow 5x^2-19x=0 \\ \Leftrightarrow x(5x-19) = 0 \\ \Leftrightarrow x = 0 \vee 5x-19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{19}{5} \\ V = \Big\{ \frac{19}{5}; 0 \Big\} \\ -----------------\)
12. \(5(-4x^2-10x)=-(18x^2+50x) \\ \Leftrightarrow -20x^2-50x=-18x^2-50x \\ \Leftrightarrow -20x^2-50x+18x^2+50x= 0 \\ \Leftrightarrow -2x^2+0x=0 \\ \Leftrightarrow -2x^2=0 \\ \Leftrightarrow x^2 = \frac{0}{-2} \\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)