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

118154 Let \(p\) and \(q\) be the roots of the equation \(x^2-2 x\) \(+A=0\) and let \(r\) and \(s\) be the roots of the equation \(x^2-18 x+B=0\), If \(p\lt q\lt r\lt s\) are in
A. P. then the values of \(A\) and \(B\) are.

1 \(-3,77\)
2 \(3,-77\)
3 3,77
4 \(-3,-77\)
Complex Numbers and Quadratic Equation

118155 If \(\alpha, \beta\) are the roots of \(11 x^2+12 x-13=0\), then \(\frac{1}{\alpha^2}+\frac{1}{\beta^2}=\) ? (approximately close to)

1 4.54
2 3.54
3 2.54
4 1.54
Complex Numbers and Quadratic Equation

118156 If the expression \(x^2-11 x+a\) and \(x^2-14 x+2 a\) must have a common factor and \(x \neq 0\), then, the common factor is

1 \((x-3)\)
2 \((x-6)\)
3 \((x-8)\)
4 None of these
Complex Numbers and Quadratic Equation

118157 If \(x=\frac{\sqrt{5}+\sqrt{2}}{\sqrt{5}-\sqrt{2}}, y=\frac{\sqrt{5}-\sqrt{2}}{\sqrt{5}+\sqrt{2}}\), then \(3 x^2+4 x y-3 y^2\) is equal to

1 \(\frac{1}{3}(56 \sqrt{10}+12)\)
2 \(\frac{1}{3}(56 \sqrt{10}-12)\)
3 \(\frac{1}{3}(56+12 \sqrt{10})\)
4 None of these
Complex Numbers and Quadratic Equation

118154 Let \(p\) and \(q\) be the roots of the equation \(x^2-2 x\) \(+A=0\) and let \(r\) and \(s\) be the roots of the equation \(x^2-18 x+B=0\), If \(p\lt q\lt r\lt s\) are in
A. P. then the values of \(A\) and \(B\) are.

1 \(-3,77\)
2 \(3,-77\)
3 3,77
4 \(-3,-77\)
Complex Numbers and Quadratic Equation

118155 If \(\alpha, \beta\) are the roots of \(11 x^2+12 x-13=0\), then \(\frac{1}{\alpha^2}+\frac{1}{\beta^2}=\) ? (approximately close to)

1 4.54
2 3.54
3 2.54
4 1.54
Complex Numbers and Quadratic Equation

118156 If the expression \(x^2-11 x+a\) and \(x^2-14 x+2 a\) must have a common factor and \(x \neq 0\), then, the common factor is

1 \((x-3)\)
2 \((x-6)\)
3 \((x-8)\)
4 None of these
Complex Numbers and Quadratic Equation

118157 If \(x=\frac{\sqrt{5}+\sqrt{2}}{\sqrt{5}-\sqrt{2}}, y=\frac{\sqrt{5}-\sqrt{2}}{\sqrt{5}+\sqrt{2}}\), then \(3 x^2+4 x y-3 y^2\) is equal to

1 \(\frac{1}{3}(56 \sqrt{10}+12)\)
2 \(\frac{1}{3}(56 \sqrt{10}-12)\)
3 \(\frac{1}{3}(56+12 \sqrt{10})\)
4 None of these
Complex Numbers and Quadratic Equation

118154 Let \(p\) and \(q\) be the roots of the equation \(x^2-2 x\) \(+A=0\) and let \(r\) and \(s\) be the roots of the equation \(x^2-18 x+B=0\), If \(p\lt q\lt r\lt s\) are in
A. P. then the values of \(A\) and \(B\) are.

1 \(-3,77\)
2 \(3,-77\)
3 3,77
4 \(-3,-77\)
Complex Numbers and Quadratic Equation

118155 If \(\alpha, \beta\) are the roots of \(11 x^2+12 x-13=0\), then \(\frac{1}{\alpha^2}+\frac{1}{\beta^2}=\) ? (approximately close to)

1 4.54
2 3.54
3 2.54
4 1.54
Complex Numbers and Quadratic Equation

118156 If the expression \(x^2-11 x+a\) and \(x^2-14 x+2 a\) must have a common factor and \(x \neq 0\), then, the common factor is

1 \((x-3)\)
2 \((x-6)\)
3 \((x-8)\)
4 None of these
Complex Numbers and Quadratic Equation

118157 If \(x=\frac{\sqrt{5}+\sqrt{2}}{\sqrt{5}-\sqrt{2}}, y=\frac{\sqrt{5}-\sqrt{2}}{\sqrt{5}+\sqrt{2}}\), then \(3 x^2+4 x y-3 y^2\) is equal to

1 \(\frac{1}{3}(56 \sqrt{10}+12)\)
2 \(\frac{1}{3}(56 \sqrt{10}-12)\)
3 \(\frac{1}{3}(56+12 \sqrt{10})\)
4 None of these
Complex Numbers and Quadratic Equation

118154 Let \(p\) and \(q\) be the roots of the equation \(x^2-2 x\) \(+A=0\) and let \(r\) and \(s\) be the roots of the equation \(x^2-18 x+B=0\), If \(p\lt q\lt r\lt s\) are in
A. P. then the values of \(A\) and \(B\) are.

1 \(-3,77\)
2 \(3,-77\)
3 3,77
4 \(-3,-77\)
Complex Numbers and Quadratic Equation

118155 If \(\alpha, \beta\) are the roots of \(11 x^2+12 x-13=0\), then \(\frac{1}{\alpha^2}+\frac{1}{\beta^2}=\) ? (approximately close to)

1 4.54
2 3.54
3 2.54
4 1.54
Complex Numbers and Quadratic Equation

118156 If the expression \(x^2-11 x+a\) and \(x^2-14 x+2 a\) must have a common factor and \(x \neq 0\), then, the common factor is

1 \((x-3)\)
2 \((x-6)\)
3 \((x-8)\)
4 None of these
Complex Numbers and Quadratic Equation

118157 If \(x=\frac{\sqrt{5}+\sqrt{2}}{\sqrt{5}-\sqrt{2}}, y=\frac{\sqrt{5}-\sqrt{2}}{\sqrt{5}+\sqrt{2}}\), then \(3 x^2+4 x y-3 y^2\) is equal to

1 \(\frac{1}{3}(56 \sqrt{10}+12)\)
2 \(\frac{1}{3}(56 \sqrt{10}-12)\)
3 \(\frac{1}{3}(56+12 \sqrt{10})\)
4 None of these