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Roots Of Quadratic

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

MathematicsWhat are the roots of the equation \(x^2-(u+2v)x+2uv=0\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Expert MathematicsFor the quadratic equation \(ax^2+bx+c=0\), where \(a\neq0\) and \(c\neq0\), which condition is necessary and sufficient for its two roots to be reciprocals of each other?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Expert MathematicsIf the product of the roots of the equation \(x^2-2(a-3)x+a^2-16=0\) is zero, what are the values of \(a\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Expert MathematicsWhat is the positive difference between the two roots of the quadratic equation \(x^2-2tx+t^2-49=0\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Expert MathematicsIf the sum of the roots of a quadratic equation is 7 and their product is 10, which is its monic quadratic equation?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Expert MathematicsWhat is the positive difference between the two roots of \\(x^2-2kx+k^2-25=0\\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Expert 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 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 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 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 \(x^2+6x+8=0\), what is the value of \((\alpha-\beta)^2+2\alpha\beta\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Expert MathematicsIf the two roots of the quadratic equation \(ax^2+bx+c=0\), where \(a\ne0\), are reciprocals of each other, which relation among the coefficients is necessary?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Expert MathematicsIf the product of the roots of the equation \(x^2-2(a+1)x+a^2-1=0\) is zero, which values of \(a\) are possible?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Expert MathematicsIf the two roots of the quadratic equation \(x^2+(m-5)x+9=0\) are equal and not of opposite signs, what are the possible values of \(m\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Expert MathematicsFor the equation \(4x^2-4(a-1)x+a^2-4a=0\) to have real roots, what is the correct condition on \(a\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Expert MathematicsIf the roots of (x^2+px+12=0) are (r) and (r+1), what are the possible values of (p)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Expert MathematicsIf the quadratic equation \(2x^2+\lambda x+8=0\) has equal roots, what can be the values of \(\lambda\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Hard MathematicsIf the two roots of the quadratic equation \(x^2+bx+c=0\) are opposites of each other, which of the following conditions is necessary?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Hard MathematicsFor the quadratic equation \(ax^2+bx+c=0\), where \(a\ne0\), when will its roots be reciprocals of each other?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Hard