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Quadratic Equations

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

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 MathematicsWhat is the nature of the roots of the quadratic equation \(x^2+2(2-\sqrt{5})x+9=0\)?Class 10Quadratic EquationsNature of RootsLevel 38Expert MathematicsIf the discriminant of a quadratic equation is \(D=36-9h^2\), what values of \(h\) will give equal roots?Class 10Quadratic EquationsNature of RootsLevel 38Expert MathematicsIf 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 38Expert MathematicsIf the discriminant of a quadratic equation is \(D=(z-4)(z+6)\), which interval of \(z\) results in no real roots of the equation?Class 10Quadratic EquationsNature of RootsLevel 38Expert MathematicsIf the discriminant of a quadratic equation is \(D=(w+2)^2\), what must be the value of \(w\) for the equation to have equal roots?Class 10Quadratic EquationsNature of RootsLevel 38Expert MathematicsA student claims that the equation \(x^2+(m-4)x+m=0\) will have equal real roots only for \(m=4\), because the coefficient of \(x\) becomes zero. Which is the correct evaluation of this claim?Class 10Quadratic EquationsNature of RootsLevel 38Expert