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Quadratic Equations

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

MathematicsIf one root of the equation \(3x^2-(3h+1)x+h=0\) is \(\frac{1}{3}\), what is the other root?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Expert MathematicsIf the roots of the quadratic equation \(x^2+px+q=0\) are \(-3\) and \(7\), what is the value of \(p-q\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Expert MathematicsIf \(\alpha\) and \(\beta\) are the roots of the equation \(x^2+8x+12=0\), what is the value of \((\alpha-\beta)^2+3\alpha\beta\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Expert MathematicsIf the roots of the equation \(x^2-(2a+7)x+(a+3)(a+4)=0\) are consecutive integers, which pair represents the roots?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Expert MathematicsIf both roots of the equation \(x^2-12x+m=0\) are prime numbers, what is the value of \(m\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Expert MathematicsWhat are the roots of the equation \(x^2-(u-v)x-uv=0\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Expert MathematicsIf the roots of the equation x² − 14x + q = 0 are in the ratio 3:4, what is the value of q?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 \(\alpha\) and \(\beta\) are the roots of the equation \(x^2-8x+n=0\) and \(\alpha^2+\beta^2=40\), what is the value of \(n\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Expert MathematicsIf the product of the roots of the equation \(x^2-2(a-2)x+a^2-9=0\) is zero, what are the values of \(a\)?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 MathematicsWhat is the positive difference between the two roots of \(x^2-2qx+q^2-16=0\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Expert MathematicsIf the roots of the quadratic equation \(x^2+ax+b=0\) are \(3+\sqrt{2}\) and \(3-\sqrt{2}\), what is the value of \(a+b\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Expert MathematicsIf the quadratic equation \(x^2+(m+1)x+16=0\) has equal roots, what are the possible values of \(m\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Expert MathematicsIf \(\alpha\) and \(\beta\) are the roots of the equation \(x^2-7x+12=0\), what is the value of \(\frac{\alpha+1}{\alpha-1}+\frac{\beta+1}{\beta-1}\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Expert MathematicsFor the quadratic equation \(9x^2-6(a+1)x+a^2-3a=0\) to have real roots, which condition on \(a\) is necessary?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Expert MathematicsWhich statement is always true for x^2-(a+6)x+6a=0?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Hard MathematicsIf the quadratic equation \(x^2-2(a-4)x+a^2-20=0\) has equal roots, what is the value of \(a\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Expert MathematicsIf the two roots of the quadratic equation \(x^2-(u+v)x+uv=0\) are equal, which relation between \(u\) and \(v\) is correct?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Expert MathematicsAssume that \(a\) is a real number. What is the nature of the roots of the equation \(x^2-2x+(a^2+1)=0\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Expert