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Discriminant

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

MathematicsIf \(x^2-2rx+(r^2-81)=0\) is a quadratic equation and \(r\) is any real number, what will be the nature of its roots?Class 10Quadratic EquationsNature of RootsLevel 39Expert MathematicsWhat is the nature of the roots of the equation \(x^2-2(3+\sqrt{5})x+(14+6\sqrt{5})=0\)?Class 10Quadratic EquationsNature of RootsLevel 39Expert MathematicsWhat is the nature of the roots of \\(x^2+2(3-\sqrt{10})x+16=0\\)?Class 10Quadratic EquationsNature of RootsLevel 39Expert MathematicsIf a quadratic equation has discriminant D = 49 − 16h², what are the values of h for equal roots?Class 10Quadratic EquationsNature of RootsLevel 39Medium MathematicsIf the discriminant of a quadratic equation is \(D=20n-80\), what condition on \(n\) is required for the equation to have two real and distinct roots?Class 10Quadratic EquationsNature of RootsLevel 39Expert MathematicsIf the discriminant of a quadratic equation is D = (z − 9)(z + 1), which interval of z is required for the equation to have no real roots?Class 10Quadratic EquationsNature of RootsLevel 39Expert MathematicsIf the discriminant of a quadratic equation is \(D=(m-8)^2\), what must be the value of \(m\) for the equation to have equal roots?Class 10Quadratic EquationsNature of RootsLevel 39Expert MathematicsIf the two possible values of the discriminant of a quadratic equation are \\(D_1=(y+5)^2\\) and \\(D_2=-(y+5)^2\\), with \\(y\neq -5\\), which case gives two distinct real roots?Class 10Quadratic EquationsNature of RootsLevel 39Expert 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 MathematicsIf the quadratic equation \(x^2+2(m-5)x+(m^2-9m+24)=0\) has equal roots, what is the value of \(m\)?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