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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।

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 MathematicsA student writes D=16 for x²−2(k−2)x+k²=0. What is the correct discriminant D?Class 10Quadratic EquationsNature of RootsLevel 38Medium MathematicsAssertion: The graph of the quadratic equation \(2x^2-4x+7=0\) does not intersect the \(x\)-axis. Reason: The discriminant of this equation is \(D=-40\). Choose the correct option.Class 10Quadratic EquationsNature of RootsLevel 38Expert MathematicsAssertion: In the equation \(x^2-2(a-b)x+(a+b)^2=0\), if \(ab<0\), its roots are real and distinct. Reason: The discriminant of this equation is \(D=-16ab\). Choose the correct option.Class 10Quadratic EquationsNature of RootsLevel 38Expert MathematicsIf \(x^2-2px+(p^2+16)=0\), what will be the nature of its roots for any real value of \(p\)?Class 10Quadratic EquationsNature of RootsLevel 38Expert MathematicsIf x² − 2px + (p² − 25) = 0, what is the nature of the roots for any real value of p?Class 10Quadratic EquationsNature of RootsLevel 38Medium MathematicsWhich of the following quadratic equations has one positive root and one negative root?Class 10Quadratic EquationsNature of RootsLevel 38Expert MathematicsIf the roots of the equation \(x^2+2(m-4)x+(m^2-7m+14)=0\) are real, which condition on \(m\) is correct?Class 10Quadratic EquationsNature of RootsLevel 38Expert MathematicsThe equation \(x^2-2(3t+1)x+(5t^2+2t+4)=0\) has no real roots. What is the correct interval for \(t\)?Class 10Quadratic EquationsNature of RootsLevel 38Expert MathematicsIf the equation \(x^2-2\mu x+2\mu=0\) has two real and distinct roots, which condition on \(\mu\) is correct?Class 10Quadratic EquationsNature of RootsLevel 38Expert MathematicsWhich option is correct about the roots of 2x² − 3√2 x + 7 = 0?Class 10Quadratic EquationsNature of RootsLevel 38Medium MathematicsWhat is the nature of the roots of the equation \\(7x^2-2\\sqrt{21}x+3=0\\)?Class 10Quadratic EquationsNature of RootsLevel 38Expert MathematicsIf \(a>0\), \(c<0\), and \(b\) is any real number, what will be the nature of the roots of the quadratic equation \(ax^2+bx+c=0\)?Class 10Quadratic EquationsNature of RootsLevel 38Expert MathematicsIf a and b are real numbers, which is the correct condition for the equation \(x^2-2(a-b)x+(a+b)^2=0\) to have real roots?Class 10Quadratic EquationsNature of RootsLevel 38Expert MathematicsWhat is the correct condition on \(t\) for the equation \(x^2+2(t+1)x+(3t+7)=0\) to have no real roots?Class 10Quadratic EquationsNature of RootsLevel 38Expert