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Discriminant

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

MathematicsIf \(\alpha\) and \(\beta\) are the roots of the equation \(x^2-10x+25=0\), what is the value of \(\alpha-\beta\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Hard MathematicsHow many real roots does the equation \(x^2+2x+5=0\) have?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Hard MathematicsIf the quadratic equation \(kx^2-6x+9=0\) has equal roots and \(k\ne0\), what is the value of \(k\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Hard MathematicsIf the roots of the quadratic equation \(x^2-4x+k=0\) are real and equal, what is the value of \(k\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Hard MathematicsWhat is the nature of the roots of the equation \(x^2-2kx+k^2=0\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Hard MathematicsWhat is the necessary and sufficient condition on \(k\) for the equation \(x^2+6x+k=0\) to have real roots?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Medium MathematicsWhich of the following quadratic equations has two equal real roots?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Medium MathematicsIf 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 33Medium MathematicsWhat is the repeated root of the equation \(25x^2-10x+1=0\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Medium MathematicsWhat 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 33Medium MathematicsIf a quadratic equation has \(a=1\), \(b=-20\), and \(c=100\), what are its roots?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Medium MathematicsWhat is the nature of the roots of 25x² − 30x + 9 = 0?Class 10Quadratic EquationsNature of RootsLevel 33Medium MathematicsWhich of the following quadratic equations has two distinct real roots?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Medium MathematicsWhich statement is correct about the real roots of the equation \(x^2-6x+20=0\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Medium MathematicsA 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 33Medium MathematicsWhat is the discriminant (D) of the quadratic equation \(4x^2-20x+25=0\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Medium MathematicsFor the quadratic equation \(x^2+4x+k=0\) to have real roots, which condition on \(k\) is necessary?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Medium MathematicsWhat 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 32Medium MathematicsIf 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 32Medium MathematicsWhich expression's sign is used to determine the nature of the roots of a quadratic equation?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Medium