Solution of Quadratic and Higher Degree Equations
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Complex Numbers and Quadratic Equation

118145 The equation formed by decreasing each root of \(a x^2+b x+c=0\) by 1 is \(2 x^2+b x+2=0\).

1 \(\mathrm{a}=-\mathrm{b}\)
2 \(\mathrm{b}=-\mathrm{c}\)
3 \(\mathrm{c}=-\mathrm{a}\)
4 \(b=a+c\)
EAMCET-2000
Complex Numbers and Quadratic Equation

118146 If \(a, b\) and \(c\) are in arithmetic progression, then the roots of the equation \(a x^2-2 b x+c=0\) are

1 1 and \(\frac{\mathrm{c}}{\mathrm{a}}\)
2 \(-\frac{1}{\mathrm{a}}\) and -c
3 -1 and \(-\frac{\mathrm{c}}{\mathrm{a}}\)
4 -2 and \(-\frac{\mathrm{c}}{2 \mathrm{a}}\)
WB JEE-2012
Complex Numbers and Quadratic Equation

118147 The number of solutions of the equation \(\log _2\left(x^2+2 x-1\right)=1\) is

1 0
2 1
3 2
4 3
WB JEE-2012
Complex Numbers and Quadratic Equation

118148 If \(\alpha, \beta\) are the roots of the quadratic equation \(x^2+p x+q=0\), then the values of \(\alpha^3+\beta^3\) and \(\alpha^4+\alpha^2 \beta^2+\beta^4\) are respectively

1 \(3 p q-p^3\) and \(p^4-3 p^2+3 q^2\)
2 \(-P\left(3 q-p^2\right)\) and \(\left(p^2-q\right)\left(p^2+3 q\right)\)
3 \(\mathrm{pq}-4\) and \(\mathrm{p}^4-\mathrm{q}^4\)
4 \(3 p q-p^3\) and \(\left(p^2-q\right)\left(p^2-3 q\right)\)
WB JEE-2014
Complex Numbers and Quadratic Equation

118149 The value of a for which the sum of the squares of the roots of the equation \(x^2-(a-2) x-a-1=\) 0 assumes the least value is

1 0
2 1
3 2
4 3
WB JEE-2022
NEET DIGITAL LIBRARY
Complex Numbers and Quadratic Equation

118145 The equation formed by decreasing each root of \(a x^2+b x+c=0\) by 1 is \(2 x^2+b x+2=0\).

1 \(\mathrm{a}=-\mathrm{b}\)
2 \(\mathrm{b}=-\mathrm{c}\)
3 \(\mathrm{c}=-\mathrm{a}\)
4 \(b=a+c\)
EAMCET-2000
Complex Numbers and Quadratic Equation

118146 If \(a, b\) and \(c\) are in arithmetic progression, then the roots of the equation \(a x^2-2 b x+c=0\) are

1 1 and \(\frac{\mathrm{c}}{\mathrm{a}}\)
2 \(-\frac{1}{\mathrm{a}}\) and -c
3 -1 and \(-\frac{\mathrm{c}}{\mathrm{a}}\)
4 -2 and \(-\frac{\mathrm{c}}{2 \mathrm{a}}\)
WB JEE-2012
Complex Numbers and Quadratic Equation

118147 The number of solutions of the equation \(\log _2\left(x^2+2 x-1\right)=1\) is

1 0
2 1
3 2
4 3
WB JEE-2012
Complex Numbers and Quadratic Equation

118148 If \(\alpha, \beta\) are the roots of the quadratic equation \(x^2+p x+q=0\), then the values of \(\alpha^3+\beta^3\) and \(\alpha^4+\alpha^2 \beta^2+\beta^4\) are respectively

1 \(3 p q-p^3\) and \(p^4-3 p^2+3 q^2\)
2 \(-P\left(3 q-p^2\right)\) and \(\left(p^2-q\right)\left(p^2+3 q\right)\)
3 \(\mathrm{pq}-4\) and \(\mathrm{p}^4-\mathrm{q}^4\)
4 \(3 p q-p^3\) and \(\left(p^2-q\right)\left(p^2-3 q\right)\)
WB JEE-2014
Complex Numbers and Quadratic Equation

118149 The value of a for which the sum of the squares of the roots of the equation \(x^2-(a-2) x-a-1=\) 0 assumes the least value is

1 0
2 1
3 2
4 3
WB JEE-2022
Join With Us for More Updates
Complex Numbers and Quadratic Equation

118145 The equation formed by decreasing each root of \(a x^2+b x+c=0\) by 1 is \(2 x^2+b x+2=0\).

1 \(\mathrm{a}=-\mathrm{b}\)
2 \(\mathrm{b}=-\mathrm{c}\)
3 \(\mathrm{c}=-\mathrm{a}\)
4 \(b=a+c\)
EAMCET-2000
Complex Numbers and Quadratic Equation

118146 If \(a, b\) and \(c\) are in arithmetic progression, then the roots of the equation \(a x^2-2 b x+c=0\) are

1 1 and \(\frac{\mathrm{c}}{\mathrm{a}}\)
2 \(-\frac{1}{\mathrm{a}}\) and -c
3 -1 and \(-\frac{\mathrm{c}}{\mathrm{a}}\)
4 -2 and \(-\frac{\mathrm{c}}{2 \mathrm{a}}\)
WB JEE-2012
Complex Numbers and Quadratic Equation

118147 The number of solutions of the equation \(\log _2\left(x^2+2 x-1\right)=1\) is

1 0
2 1
3 2
4 3
WB JEE-2012
Complex Numbers and Quadratic Equation

118148 If \(\alpha, \beta\) are the roots of the quadratic equation \(x^2+p x+q=0\), then the values of \(\alpha^3+\beta^3\) and \(\alpha^4+\alpha^2 \beta^2+\beta^4\) are respectively

1 \(3 p q-p^3\) and \(p^4-3 p^2+3 q^2\)
2 \(-P\left(3 q-p^2\right)\) and \(\left(p^2-q\right)\left(p^2+3 q\right)\)
3 \(\mathrm{pq}-4\) and \(\mathrm{p}^4-\mathrm{q}^4\)
4 \(3 p q-p^3\) and \(\left(p^2-q\right)\left(p^2-3 q\right)\)
WB JEE-2014
Complex Numbers and Quadratic Equation

118149 The value of a for which the sum of the squares of the roots of the equation \(x^2-(a-2) x-a-1=\) 0 assumes the least value is

1 0
2 1
3 2
4 3
WB JEE-2022
For More Updates join with Us
Complex Numbers and Quadratic Equation

118145 The equation formed by decreasing each root of \(a x^2+b x+c=0\) by 1 is \(2 x^2+b x+2=0\).

1 \(\mathrm{a}=-\mathrm{b}\)
2 \(\mathrm{b}=-\mathrm{c}\)
3 \(\mathrm{c}=-\mathrm{a}\)
4 \(b=a+c\)
EAMCET-2000
Complex Numbers and Quadratic Equation

118146 If \(a, b\) and \(c\) are in arithmetic progression, then the roots of the equation \(a x^2-2 b x+c=0\) are

1 1 and \(\frac{\mathrm{c}}{\mathrm{a}}\)
2 \(-\frac{1}{\mathrm{a}}\) and -c
3 -1 and \(-\frac{\mathrm{c}}{\mathrm{a}}\)
4 -2 and \(-\frac{\mathrm{c}}{2 \mathrm{a}}\)
WB JEE-2012
Complex Numbers and Quadratic Equation

118147 The number of solutions of the equation \(\log _2\left(x^2+2 x-1\right)=1\) is

1 0
2 1
3 2
4 3
WB JEE-2012
Complex Numbers and Quadratic Equation

118148 If \(\alpha, \beta\) are the roots of the quadratic equation \(x^2+p x+q=0\), then the values of \(\alpha^3+\beta^3\) and \(\alpha^4+\alpha^2 \beta^2+\beta^4\) are respectively

1 \(3 p q-p^3\) and \(p^4-3 p^2+3 q^2\)
2 \(-P\left(3 q-p^2\right)\) and \(\left(p^2-q\right)\left(p^2+3 q\right)\)
3 \(\mathrm{pq}-4\) and \(\mathrm{p}^4-\mathrm{q}^4\)
4 \(3 p q-p^3\) and \(\left(p^2-q\right)\left(p^2-3 q\right)\)
WB JEE-2014
Complex Numbers and Quadratic Equation

118149 The value of a for which the sum of the squares of the roots of the equation \(x^2-(a-2) x-a-1=\) 0 assumes the least value is

1 0
2 1
3 2
4 3
WB JEE-2022
NEET DIGITAL LIBRARY
Complex Numbers and Quadratic Equation

118145 The equation formed by decreasing each root of \(a x^2+b x+c=0\) by 1 is \(2 x^2+b x+2=0\).

1 \(\mathrm{a}=-\mathrm{b}\)
2 \(\mathrm{b}=-\mathrm{c}\)
3 \(\mathrm{c}=-\mathrm{a}\)
4 \(b=a+c\)
EAMCET-2000
Complex Numbers and Quadratic Equation

118146 If \(a, b\) and \(c\) are in arithmetic progression, then the roots of the equation \(a x^2-2 b x+c=0\) are

1 1 and \(\frac{\mathrm{c}}{\mathrm{a}}\)
2 \(-\frac{1}{\mathrm{a}}\) and -c
3 -1 and \(-\frac{\mathrm{c}}{\mathrm{a}}\)
4 -2 and \(-\frac{\mathrm{c}}{2 \mathrm{a}}\)
WB JEE-2012
Complex Numbers and Quadratic Equation

118147 The number of solutions of the equation \(\log _2\left(x^2+2 x-1\right)=1\) is

1 0
2 1
3 2
4 3
WB JEE-2012
Complex Numbers and Quadratic Equation

118148 If \(\alpha, \beta\) are the roots of the quadratic equation \(x^2+p x+q=0\), then the values of \(\alpha^3+\beta^3\) and \(\alpha^4+\alpha^2 \beta^2+\beta^4\) are respectively

1 \(3 p q-p^3\) and \(p^4-3 p^2+3 q^2\)
2 \(-P\left(3 q-p^2\right)\) and \(\left(p^2-q\right)\left(p^2+3 q\right)\)
3 \(\mathrm{pq}-4\) and \(\mathrm{p}^4-\mathrm{q}^4\)
4 \(3 p q-p^3\) and \(\left(p^2-q\right)\left(p^2-3 q\right)\)
WB JEE-2014
Complex Numbers and Quadratic Equation

118149 The value of a for which the sum of the squares of the roots of the equation \(x^2-(a-2) x-a-1=\) 0 assumes the least value is

1 0
2 1
3 2
4 3
WB JEE-2022