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Rational Roots

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

MathematicsIf x² − 2rx + (r² − 49) = 0, what is the nature of the roots for any real value of r?Class 10Quadratic EquationsNature of RootsLevel 38Medium MathematicsIf x² - 2rx + (r² - 16) = 0, what is the nature of the roots for any real value of r?Class 10Quadratic EquationsNature of RootsLevel 37Medium MathematicsWhat is the nature of roots of (6x^2-11x+3=0)?Class 10Quadratic EquationsNature of RootsLevel 39Hard MathematicsWhat is the nature and type of roots of (x^2-7x+10=0)?Class 10Quadratic EquationsNature of RootsLevel 39Hard MathematicsWhat is the nature of the roots of the equation \(x^2-19x+90=0\)?Class 10Quadratic EquationsNature of RootsLevel 39Medium MathematicsA number-related problem leads to the equation \(n^2-21n+110=0\). What is the nature of the roots of this equation?Class 10Quadratic EquationsNature of RootsLevel 39Medium MathematicsFor a quadratic equation with rational coefficients, if the discriminant is \(\Delta=144\), which statement correctly describes the nature of its roots?Class 10Quadratic EquationsNature of RootsLevel 39Medium MathematicsWhat is the nature of the roots of the equation \\(10x^2-19x+6=0\\)?Class 10Quadratic EquationsNature of RootsLevel 39Medium MathematicsWhat is the nature of the roots of the equation \\(8x^2+2x-3=0\\)?Class 10Quadratic EquationsNature of RootsLevel 39Medium MathematicsWhich of the following equations has two real, rational and distinct roots?Class 10Quadratic EquationsNature of RootsLevel 39Medium MathematicsWhat is the nature of the roots of the equation \\(6x^2-13x+6=0\\)?Class 10Quadratic EquationsNature of RootsLevel 39Medium MathematicsWhat is the nature of the roots of the equation \(4x^2+7x-2=0\)?Class 10Quadratic EquationsNature of RootsLevel 39Medium MathematicsWhat is the nature of the roots of \(2x^2-11x+15=0\)?Class 10Quadratic EquationsNature of RootsLevel 38Medium MathematicsIf \(a\) is a real parameter and \(x^2-2(a+4)x+a^2+8a+15=0\), what will be the nature of its roots?Class 10Quadratic EquationsNature of RootsLevel 38Hard MathematicsWhat is the nature of the roots of x² − (2r+5)x + (r²+5r+4) = 0?Class 10Quadratic EquationsNature of RootsLevel 38Hard MathematicsWhat is the nature of the roots of the quadratic equation \(x^2-13x+40=0\)?Class 10Quadratic EquationsNature of RootsLevel 38Medium MathematicsA number-related problem leads to the equation \(n^2-15n+56=0\). What is the nature of the roots of this quadratic equation?Class 10Quadratic EquationsNature of RootsLevel 38Medium MathematicsFor a quadratic equation \(ax^2+bx+c=0\), where \(a,b,c\) are rational numbers and \(a\ne0\), if the discriminant \(D=b^2-4ac=100\), which statement correctly describes the roots?Class 10Quadratic EquationsNature of RootsLevel 38Medium MathematicsWhat is the nature of the roots of the equation \(7x^2-9x+2=0\)?Class 10Quadratic EquationsNature of RootsLevel 38Medium MathematicsWhat is the discriminant of \\(x^2+9x+14=0\\), and what is the nature of its roots?Class 10Quadratic EquationsNature of RootsLevel 38Medium