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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 discriminant \(D\) of the quadratic equation \(x^2-2(k-3)x+k^2=0\)?Class 10Quadratic EquationsNature of RootsLevel 39Expert MathematicsAssertion: The graph of the parabola \(y=3x^2-6x+11\) does not intersect the \(x\)-axis. Reason: The discriminant of the corresponding quadratic equation is \(D=-96\). Choose the correct option.Class 10Quadratic EquationsNature of RootsLevel 39Expert MathematicsAssertion: In the equation \(x^2-2(a-3b)x+(a+3b)^2=0\), if \(ab<0\), then its roots are real and distinct. Reason: The discriminant of this equation is \(D=-48ab\). Choose the correct option.Class 10Quadratic EquationsNature of RootsLevel 39Expert MathematicsFor the quadratic equation \(x^2-2px+(p^2+36)=0\), what is the correct conclusion about the nature of its roots for any real value of \(p\)?Class 10Quadratic EquationsNature of RootsLevel 39Expert MathematicsIf x² − 2px + (p² − 64) = 0, what is the nature of the roots for any real value of p?Class 10Quadratic EquationsNature of RootsLevel 39Medium MathematicsIf \(p\) is any real number, what is the nature of the roots of the equation \(x^2+2px+(p^2+1)=0\)?Class 10Quadratic EquationsNature of RootsLevel 39Expert MathematicsIf m is a real number and the equation x² + 2(m − 5)x + (m² − 9m + 24) = 0 has no real roots, which condition on m is correct?Class 10Quadratic EquationsNature of RootsLevel 39Expert MathematicsThe equation \(x^2-2(4t+1)x+(7t^2+2t+5)=0\) has no real roots. Which is the correct interval for \(t\)?Class 10Quadratic EquationsNature of RootsLevel 39Expert MathematicsFor which values of \(\theta\) does the quadratic equation \(x^2-2\theta x+3\theta=0\) have equal roots?Class 10Quadratic EquationsNature of RootsLevel 39Expert MathematicsIf the equation \(x^2-2\theta x+3\theta=0\) has two real and distinct roots, which condition on \(\theta\) is correct?Class 10Quadratic EquationsNature of RootsLevel 39Expert MathematicsWhich option is correct about the roots of 5x² − 3√5x + 6 = 0?Class 10Quadratic EquationsNature of RootsLevel 39Medium MathematicsWhat is the nature of the roots of \\(8x^2-4\sqrt{10}x+5=0\\)?Class 10Quadratic EquationsNature of RootsLevel 39Expert MathematicsIf \(a<0\), \(c<0\), and \(b=0\), what is the nature of the roots of the quadratic equation \(ax^2+c=0\)?Class 10Quadratic EquationsNature of RootsLevel 39Expert 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 39Expert MathematicsIf \(a\) and \(b\) are real numbers, which condition is necessary and sufficient for the equation \(x^2-2(a-2b)x+(a+2b)^2=0\) to have real roots?Class 10Quadratic EquationsNature of RootsLevel 39Expert MathematicsIf \(a\) and \(b\) are real numbers and the roots of \(x^2-2(a+b)x+3ab=0\) are real, which statement about \(a\) and \(b\) is correct?Class 10Quadratic EquationsNature of RootsLevel 39Expert MathematicsWhat is the correct condition on \(v\) for the equation \(x^2+2(v+2)x+(4v+11)=0\) to have no real roots?Class 10Quadratic EquationsNature of RootsLevel 39Expert MathematicsFor the equation \((q+3)x^2-2(q-2)x+q=0\), what is the value of \(q\) for which the roots are equal, given that \(q\ne -3\)?Class 10Quadratic EquationsNature of RootsLevel 39Expert MathematicsIf p ≠ 2 in (p − 2)x² − 2(p + 2)x + (p + 6) = 0, what is the condition on p for real roots?Class 10Quadratic EquationsNature of RootsLevel 39Hard MathematicsFor the quadratic equation \(x^2-(u+6)x+6u=0\) to have equal roots, what must be the value of \(u\)?Class 10Quadratic EquationsNature of RootsLevel 39Expert