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Distinct Roots

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

MathematicsIf \\(m+4)x^2-2(m+2)x+m=0\\) with \\(m\ne -4\\), what will be the nature of its roots?Class 10Quadratic EquationsNature of RootsLevel 39ExpertMathematicsWhich condition is required for the equation \(x^2-(t+7)x+7t=0\) to have two real and distinct roots?Class 10Quadratic EquationsNature of RootsLevel 39ExpertMathematicsIf the discriminant of a quadratic equation is \(D=12n-36\), what condition on \(n\) is necessary for the equation to have two real and distinct roots?Class 10Quadratic EquationsNature of RootsLevel 38ExpertMathematicsIf \\(x^2-(2a+1)x+a(a+1)=0\\), where \\(a\\) is a real parameter, what will be the nature of its roots?Class 10Quadratic EquationsNature of RootsLevel 37ExpertMathematicsA number puzzle gives the equation \(n^2-2pn+(p^2-5p)=0\). What condition on \(p\) is necessary for the equation to have two real and distinct values of \(n\)?Class 10Quadratic EquationsNature of RootsLevel 37ExpertMathematicsLet \(p\) and \(q\) be real numbers. If \(x^2-2px+(p^2-q^2)=0\) and \(q\neq 0\), what is the nature of the roots of this quadratic equation?Class 10Quadratic EquationsNature of RootsLevel 37ExpertMathematicsIf (x^2-2\lambda x+\lambda=0) has two real and distinct roots, which condition on (\lambda) is correct?Class 10Quadratic EquationsNature of RootsLevel 37ExpertMathematicsWhich condition on \(k\) is required for the equation \(x^2-16x+k=0\) to have two real and distinct roots?Class 10Quadratic EquationsNature of RootsLevel 39MediumMathematicsWhich of the following quadratic equations has two real and distinct roots?Class 10Quadratic EquationsNature of RootsLevel 38MediumMathematicsWhich condition on \(k\) is necessary for the equation \(x^2-12x+k=0\) to have two real and distinct roots?Class 10Quadratic EquationsNature of RootsLevel 38MediumMathematicsIf \(a\) is a real number, what is the nature of the roots of the equation \(2x^2-4ax+(2a^2-3)=0\)?Class 10Quadratic EquationsNature of RootsLevel 37HardMathematicsWhat is the nature of the roots of the equation \(6x^2-5x+1=0\)?Class 10Quadratic EquationsNature of RootsLevel 39EasyMathematicsStatement: If the discriminant \(D<0\), the equation has two real and distinct roots. What type of statement is this?Class 10Quadratic EquationsNature of RootsLevel 39EasyMathematicsWhat is the nature of the roots of the quadratic equation \(x^2-2x-1=0\)?Class 10Quadratic EquationsNature of RootsLevel 39EasyMathematicsWhat is the nature of the roots of the equation \(x^2-6x+8=0\)?Class 10Quadratic EquationsNature of RootsLevel 39EasyMathematicsWhat is the nature of the roots of \(3x^2-5x+2=0\)?Class 10Quadratic EquationsNature of RootsLevel 39EasyMathematicsWhat is the nature of roots of the equation (7x^2-10x+3=0)?Class 10Quadratic EquationsNature of RootsLevel 38EasyMathematicsWhich of the following quadratic equations has real and distinct roots?Class 10Quadratic EquationsNature of RootsLevel 38EasyMathematicsWhich pair correctly gives the discriminant \(\Delta\) and the nature of the roots of \(x^2+5x+6=0\)?Class 10Quadratic EquationsNature of RootsLevel 37EasyMathematicsFor (x^2-2x+n=0) to have two real and distinct roots, which condition is correct?Class 10Quadratic EquationsNature of RootsLevel 37Easy