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Nature Of Roots

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

MathematicsWhich 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 39Expert MathematicsIf x² − 2(k − 4)x + (k² − 10k + 27) = 0 has no real roots, which condition on k is correct?Class 10Quadratic EquationsNature of RootsLevel 39Hard MathematicsFor a quadratic equation \(ax^2+bx+c=0\) with real coefficients, where \(a\ne0\), which condition identifies that its roots have opposite signs?Class 10Quadratic EquationsNature of RootsLevel 39Expert MathematicsWhat is the nature of the roots of the equation \(3x^2-2\sqrt{21}x+7=0\)?Class 10Quadratic EquationsNature of RootsLevel 39Expert MathematicsChoose the correct conclusion about the nature of the roots of \(2x^2-5\sqrt{2}x+8=0\).Class 10Quadratic EquationsNature of RootsLevel 39Expert MathematicsWhat is the nature of the roots of the equation \(6x^2-4\sqrt{6}x+4=0\)?Class 10Quadratic EquationsNature of RootsLevel 39Expert MathematicsIf D = b² − 4ac is positive but not a perfect square, what is the most accurate nature of the roots of ax² + bx + c = 0?Class 10Quadratic EquationsNature of RootsLevel 39Medium MathematicsWhat is the nature of the roots of \(x^2-2(1+\sqrt{5})x+(6+2\sqrt{5})=0\)?Class 10Quadratic EquationsNature of RootsLevel 38Expert MathematicsIf the discriminant of a quadratic equation is ( D=-(p-1)^2 ) and ( p\ne 1 ), what is the nature of its roots?Class 10Quadratic EquationsNature of RootsLevel 38Expert MathematicsFor which values of \(k\) will the quadratic equation \(x^2-2(k+1)x+(k^2+1)=0\) have two distinct real roots?Class 10Quadratic EquationsNature of RootsLevel 38Expert MathematicsIf the equation \(x^2-2(a+2)x+(a^2+6a+8)=0\) has no real roots, which condition on \(a\) is correct?Class 10Quadratic EquationsNature of RootsLevel 38Expert MathematicsIf \(a,b,c\) are integers and \(a\ne0\), which condition identifies that the quadratic equation \(ax^2+bx+c=0\) has two distinct irrational real roots?Class 10Quadratic EquationsNature of RootsLevel 38Expert MathematicsFor the equation \(n^2-2pn+(p^2-7p)=0\), what condition on \(p\) is necessary for \(n\) to have two real and distinct roots?Class 10Quadratic EquationsNature of RootsLevel 38Expert MathematicsA geometric situation leads to the quadratic equation \(L^2-2(a+4)L+(a^2+6a+13)=0\). What condition on \(a\) is necessary for \(L\) to have real values?Class 10Quadratic EquationsNature of RootsLevel 38Expert MathematicsFor the parabola \(y=x^2-2kx+(k^2-9)\), where \(k\) is any real number, how will it intersect the \(x\)-axis?Class 10Quadratic EquationsNature of RootsLevel 38Expert MathematicsHow will the parabola \(y=x^2-2(k-1)x+(k-1)^2\) meet the \(x\)-axis?Class 10Quadratic EquationsNature of RootsLevel 38Expert MathematicsHow many points of intersection are there between the parabola \(y=x^2-2kx+k^2+4\) and the x-axis?Class 10Quadratic EquationsNature of RootsLevel 38Expert MathematicsFor the equation \(x^2-2rx+(r^2+25)=0\), where \(r\) is any real number, what is the correct conclusion about the nature of its roots?Class 10Quadratic EquationsNature of RootsLevel 38Expert 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 MathematicsWhat is the nature of the roots of the equation \(x^2-2(2+\sqrt{3})x+(7+4\sqrt{3})=0\)?Class 10Quadratic EquationsNature of RootsLevel 38Expert