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Quadratic Roots

Class 10 Mathematics के इस tag से जुड़े questions। हर question के साथ chapter, topic, level और difficulty दी गई है।

MathematicsIf (\alpha,\beta) are roots of (x^2-4x+1=0), what is (\alpha^4+\beta^4)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Expert MathematicsIf (\alpha,\beta) are roots of (x^2+5x+r=0) and (\alpha^2\beta+\alpha\beta^2=-20), what is (r)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Expert MathematicsIf the roots of (x^2-12x+q=0) are in the ratio (2:3), what is the value of (q)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Expert MathematicsIf the roots of (x^2-4x+k=0) are (\sin \theta) and (\cos \theta), what is the maximum possible value of (k)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Expert MathematicsIf (\alpha,\beta) are the roots of (x^2-9x+18=0), what is (\frac{\alpha}{\beta}+\frac{\beta}{\alpha})?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Expert MathematicsWhat is the correct conclusion about the roots of (x^2-(2a+1)x+a(a+1)=0)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Hard MathematicsIf one root of (x^2-(m+2)x+3m=0) is (3), what is the other root?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Expert MathematicsIf one root of (x^2-(m-2)x+m-6=0) is (3), what is the other root?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Expert MathematicsIf the roots of (2x^2-(3t+1)x+t^2+t=0) are (t) and (\frac{t+1}{2}), for which values is this statement true?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Expert MathematicsIf (\alpha,\beta) are the roots of (x^2-2x-8=0), what is ((\alpha+3)(\beta+3))?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Expert MathematicsIf both roots of (x^2+4x+c=0) are real and negative, which condition is necessary and sufficient?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Expert MathematicsWhich statement is correct about the roots of (x^2-2px+p^2-9=0)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Hard MathematicsIf (\alpha,\beta) are the roots of (x^2-3x-1=0), what is the correct value of (\alpha^2+3\beta+\alpha\beta)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Expert MathematicsIf (\alpha,\beta) are the roots of (x^2-3x-1=0), what is (\alpha^2+3\beta+\alpha\beta) when (\alpha) is the larger root?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Expert MathematicsIf (\alpha,\beta) are the roots of (2x^2-5x+3=0), what is (\alpha^3+\beta^3)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Expert MathematicsIf (\alpha,\beta) are the roots of (x^2-7x+10=0), what is (\frac{\alpha+2}{\alpha-2}+\frac{\beta+2}{\beta-2})?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Expert MathematicsIf (\alpha,\beta) are the roots of (x^2-8x+15=0), what is (\frac{\alpha+2}{\alpha-2}+\frac{\beta+2}{\beta-2})?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Expert MathematicsIf the roots of (kx^2-8x+k=0) are real and reciprocal, what is the correct condition on (k)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Expert MathematicsIf (\alpha,\beta) are the roots of (x^2-5x+2=0), what is (\frac{1}{\alpha^2}+\frac{1}{\beta^2})?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Expert MathematicsWhich statement is always true for (x^2-(a+4)x+4a=0)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Hard