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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 the roots of a quadratic equation are reciprocals of each other and their sum is (\frac{5}{2}), which equation is possible?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Expert MathematicsIf (\alpha,\beta) are roots of (x^2-5x+6=0), which equation has roots (\alpha+\beta) and (\alpha\beta)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Expert MathematicsIf \(\alpha\) and \(\beta\) are the roots of the equation \(x^2+x-2=0\), what is the value of \(\alpha^5+\beta^5\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Expert MathematicsIf (x^2+bx+49=0) has equal and negative roots, what is the value of (b)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Expert MathematicsIf (\alpha,\beta) are roots of (x^2-5x+c=0) and (\alpha^2+\beta^2=17), what are the roots?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Expert MathematicsWhat is the nature of the roots of (x^2-2x+(a^2+2)=0)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Expert MathematicsIf (\alpha,\beta) are roots of (x^2-6x+5=0), what is (\alpha^2-5\alpha+\beta^2-5\beta)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Expert MathematicsFor (x^2+10x+\lambda=0) to have real distinct roots and both negative roots, what is the correct condition on (\lambda)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Expert MathematicsIf (\alpha,\beta) are roots of (3x^2-13x+4=0), what is the positive value of (\alpha-\beta)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Expert MathematicsIf (x^2+px+36=0) has equal and positive roots, what is the value of (p)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Expert MathematicsIf (\alpha,\beta) are roots of (x^2-3x+1=0), what is (\alpha^4+\beta^4)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Expert MathematicsIf (\alpha,\beta) are roots of (x^2-6x+r=0) and (\alpha^2\beta+\alpha\beta^2=54), what is (r)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Expert MathematicsIf the roots of (5x^2-4x+λ=0) are not real, what is the correct condition on (λ)?Class 10Quadratic EquationsNature of RootsLevel 32Hard MathematicsIf the roots of (x^2+ax+b=0) are (\frac{1}{3+\sqrt{5}}) and (\frac{1}{3-\sqrt{5}}), what is the value of (a)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Expert MathematicsIf the roots of (x^2-sx+1=0) can be (\tan\theta) and (\cot\theta), what is the correct condition on (s) for real (\theta)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Expert MathematicsIf (\alpha,\beta) are the roots of (x^2-11x+24=0), what is (\frac{\alpha}{\beta}+\frac{\beta}{\alpha})?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Expert MathematicsWhat are the roots of the quadratic equation x² − 2(a + 1)x + a² + 2a = 0?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Expert MathematicsIf the roots of (3x^2-(4t+2)x+t(t+2)=0) are said to be (t) and (\frac{t+2}{3}), when is this statement true?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Expert MathematicsIf (\alpha,\beta) are the roots of (x^2-3x-10=0), what is ((\alpha-4)(\beta-4))?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Expert MathematicsIf both roots of (x^2-5x+c=0) are real and positive, what is the correct condition on (c)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Expert