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Equal Roots

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

MathematicsWhat is the nature of the roots of the equation \(x^2-2kx+k^2=0\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31HardMathematicsIf the roots of the equation \(x^2+ax+25=0\) are \(5\) and \(5\), what is the value of \(a\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33MediumMathematicsWhich of the following quadratic equations has two equal real roots?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33MediumMathematicsIf the discriminant of a quadratic equation is \(D=0\) and the sum of its roots is \(14\), what is the value of each root?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33MediumMathematicsWhat condition must the discriminant of a quadratic equation satisfy for it to have two real and equal roots?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33MediumMathematicsWhat is the nature of the roots of 25x² − 30x + 9 = 0?Class 10Quadratic EquationsNature of RootsLevel 33MediumMathematicsIf both roots of the equation \(x^2+px+36=0\) are \(-6\), what is the value of \(p\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33MediumMathematicsA student says that the equation \(x^2-6x+9=0\) has two distinct real roots because its discriminant is not less than zero. What is the error in the student's statement?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33MediumMathematicsWhat is the discriminant (D) of the quadratic equation \(4x^2-20x+25=0\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33MediumMathematicsIf the two roots of the equation \(x^2+ax+16=0\) are 4 and 4, what is the value of \(a\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32MediumMathematicsWhat is the condition for the quadratic equation \(ax^2+bx+c=0\), where \(a\ne0\), to have two equal real roots?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32MediumMathematicsIf the discriminant \(D=0\) and the sum of the roots is \(12\), what is the value of each root?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32MediumMathematicsThe two roots of the equation \(x^2+px+25=0\) are \(-5\) and \(-5\). What is the value of \(p\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32MediumMathematicsWhat is the discriminant \(D\) of the equation \(3x^2-6x+3=0\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32MediumMathematicsIf both roots of the equation \(x^2+ax+9=0\) are \(3\), what is the value of \(a\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31MediumMathematicsIf the discriminant \(D=0\) for a quadratic equation and the sum of its roots is 10, what is the value of each root?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31MediumMathematicsIf both roots of the equation x² + px + 16 = 0 are -4 and -4, what is the value of p?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31MediumMathematicsFor the equation \(x^2-6x+k=0\) to have two equal real roots, what should be the value of \(k\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31MediumMathematicsWhat is the discriminant \(D\) of the quadratic equation \(2x^2-4x+2=0\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31MediumMathematicsIf the discriminant of the quadratic equation \(ax^2+bx+c=0\) is zero, which statement about its roots is correct?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Medium