Solution of Quadratic and Higher Degree Equations
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NEET DIGITAL LIBRARY
Complex Numbers and Quadratic Equation

118074 If complex number \(z_1, z_2\) and 0 are vertices of equilateral triangle, then \(z_1^2+z_2^2-z_1 z_2\) is equal to

1 0
2 \(z_1-z_2\)
3 \(z_1+z_2\)
4 1
BITSAT-2015
Complex Numbers and Quadratic Equation

118075 If \(\alpha\) and \(\beta\) are roots of \(x^2-a x+b=0\) and if \(\boldsymbol{\alpha}^{\mathrm{n}}+\boldsymbol{\beta}^{\mathrm{n}}=\mathrm{V}_{\mathrm{n}}\), then

1 \(V_{n+1}=a V_n+b V_{n-1}\)
2 \(\mathrm{V}_{\mathrm{n}+1}=a \mathrm{~V}_{\mathrm{n}}+\mathrm{aV} \mathrm{V}_{\mathrm{n}-1}\)
3 \(V_{n+1}=a V_n-b V_{n-1}\)
4 \(V_{n+1}=a V_{n-1}-b V_n\)
VITEEE-2013
Complex Numbers and Quadratic Equation

118076 If \(\left|x^2-x-6\right|=x+2\), then the values of \(x\) are

1 \(-2,2,-4\)
2 \(-2,2,4\)
3 \(3,2,-2\)
4 \(4,4,3\)
VITEEE-2013
Complex Numbers and Quadratic Equation

118077 If one root is square of the other root of the equation \(\mathbf{x}^2+\mathbf{p x}+\mathbf{q}=\mathbf{0}\), then the relations between \(p\) and \(q\) is

1 \(\mathrm{p}^3-(3 \mathrm{p}-1) \mathrm{q}+\mathrm{q}^2=0\)
2 \(\mathrm{p}^3-\mathrm{q}(3 \mathrm{p}+1)+\mathrm{q}^2=0\)
3 \(\mathrm{p}^3+\mathrm{q}(3 \mathrm{p}-1)+\mathrm{q}^2=0\)
4 \(\mathrm{p}^3+\mathrm{q}(3 \mathrm{p}+1)+\mathrm{q}^2=0\)
VITEEE-2012
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Complex Numbers and Quadratic Equation

118074 If complex number \(z_1, z_2\) and 0 are vertices of equilateral triangle, then \(z_1^2+z_2^2-z_1 z_2\) is equal to

1 0
2 \(z_1-z_2\)
3 \(z_1+z_2\)
4 1
BITSAT-2015
Complex Numbers and Quadratic Equation

118075 If \(\alpha\) and \(\beta\) are roots of \(x^2-a x+b=0\) and if \(\boldsymbol{\alpha}^{\mathrm{n}}+\boldsymbol{\beta}^{\mathrm{n}}=\mathrm{V}_{\mathrm{n}}\), then

1 \(V_{n+1}=a V_n+b V_{n-1}\)
2 \(\mathrm{V}_{\mathrm{n}+1}=a \mathrm{~V}_{\mathrm{n}}+\mathrm{aV} \mathrm{V}_{\mathrm{n}-1}\)
3 \(V_{n+1}=a V_n-b V_{n-1}\)
4 \(V_{n+1}=a V_{n-1}-b V_n\)
VITEEE-2013
Complex Numbers and Quadratic Equation

118076 If \(\left|x^2-x-6\right|=x+2\), then the values of \(x\) are

1 \(-2,2,-4\)
2 \(-2,2,4\)
3 \(3,2,-2\)
4 \(4,4,3\)
VITEEE-2013
Complex Numbers and Quadratic Equation

118077 If one root is square of the other root of the equation \(\mathbf{x}^2+\mathbf{p x}+\mathbf{q}=\mathbf{0}\), then the relations between \(p\) and \(q\) is

1 \(\mathrm{p}^3-(3 \mathrm{p}-1) \mathrm{q}+\mathrm{q}^2=0\)
2 \(\mathrm{p}^3-\mathrm{q}(3 \mathrm{p}+1)+\mathrm{q}^2=0\)
3 \(\mathrm{p}^3+\mathrm{q}(3 \mathrm{p}-1)+\mathrm{q}^2=0\)
4 \(\mathrm{p}^3+\mathrm{q}(3 \mathrm{p}+1)+\mathrm{q}^2=0\)
VITEEE-2012
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NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
Complex Numbers and Quadratic Equation

118074 If complex number \(z_1, z_2\) and 0 are vertices of equilateral triangle, then \(z_1^2+z_2^2-z_1 z_2\) is equal to

1 0
2 \(z_1-z_2\)
3 \(z_1+z_2\)
4 1
BITSAT-2015
Complex Numbers and Quadratic Equation

118075 If \(\alpha\) and \(\beta\) are roots of \(x^2-a x+b=0\) and if \(\boldsymbol{\alpha}^{\mathrm{n}}+\boldsymbol{\beta}^{\mathrm{n}}=\mathrm{V}_{\mathrm{n}}\), then

1 \(V_{n+1}=a V_n+b V_{n-1}\)
2 \(\mathrm{V}_{\mathrm{n}+1}=a \mathrm{~V}_{\mathrm{n}}+\mathrm{aV} \mathrm{V}_{\mathrm{n}-1}\)
3 \(V_{n+1}=a V_n-b V_{n-1}\)
4 \(V_{n+1}=a V_{n-1}-b V_n\)
VITEEE-2013
Complex Numbers and Quadratic Equation

118076 If \(\left|x^2-x-6\right|=x+2\), then the values of \(x\) are

1 \(-2,2,-4\)
2 \(-2,2,4\)
3 \(3,2,-2\)
4 \(4,4,3\)
VITEEE-2013
Complex Numbers and Quadratic Equation

118077 If one root is square of the other root of the equation \(\mathbf{x}^2+\mathbf{p x}+\mathbf{q}=\mathbf{0}\), then the relations between \(p\) and \(q\) is

1 \(\mathrm{p}^3-(3 \mathrm{p}-1) \mathrm{q}+\mathrm{q}^2=0\)
2 \(\mathrm{p}^3-\mathrm{q}(3 \mathrm{p}+1)+\mathrm{q}^2=0\)
3 \(\mathrm{p}^3+\mathrm{q}(3 \mathrm{p}-1)+\mathrm{q}^2=0\)
4 \(\mathrm{p}^3+\mathrm{q}(3 \mathrm{p}+1)+\mathrm{q}^2=0\)
VITEEE-2012
NEET DIGITAL LIBRARY
Complex Numbers and Quadratic Equation

118074 If complex number \(z_1, z_2\) and 0 are vertices of equilateral triangle, then \(z_1^2+z_2^2-z_1 z_2\) is equal to

1 0
2 \(z_1-z_2\)
3 \(z_1+z_2\)
4 1
BITSAT-2015
Complex Numbers and Quadratic Equation

118075 If \(\alpha\) and \(\beta\) are roots of \(x^2-a x+b=0\) and if \(\boldsymbol{\alpha}^{\mathrm{n}}+\boldsymbol{\beta}^{\mathrm{n}}=\mathrm{V}_{\mathrm{n}}\), then

1 \(V_{n+1}=a V_n+b V_{n-1}\)
2 \(\mathrm{V}_{\mathrm{n}+1}=a \mathrm{~V}_{\mathrm{n}}+\mathrm{aV} \mathrm{V}_{\mathrm{n}-1}\)
3 \(V_{n+1}=a V_n-b V_{n-1}\)
4 \(V_{n+1}=a V_{n-1}-b V_n\)
VITEEE-2013
Complex Numbers and Quadratic Equation

118076 If \(\left|x^2-x-6\right|=x+2\), then the values of \(x\) are

1 \(-2,2,-4\)
2 \(-2,2,4\)
3 \(3,2,-2\)
4 \(4,4,3\)
VITEEE-2013
Complex Numbers and Quadratic Equation

118077 If one root is square of the other root of the equation \(\mathbf{x}^2+\mathbf{p x}+\mathbf{q}=\mathbf{0}\), then the relations between \(p\) and \(q\) is

1 \(\mathrm{p}^3-(3 \mathrm{p}-1) \mathrm{q}+\mathrm{q}^2=0\)
2 \(\mathrm{p}^3-\mathrm{q}(3 \mathrm{p}+1)+\mathrm{q}^2=0\)
3 \(\mathrm{p}^3+\mathrm{q}(3 \mathrm{p}-1)+\mathrm{q}^2=0\)
4 \(\mathrm{p}^3+\mathrm{q}(3 \mathrm{p}+1)+\mathrm{q}^2=0\)
VITEEE-2012
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