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

MathematicsAssertion: The graph of x² + 2x + 5 = 0 does not cut the x-axis. Reason: Its discriminant D = −16. Choose the correct option.Class 10Quadratic EquationsNature of RootsLevel 37MediumMathematicsAssertion: For 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 37ExpertMathematicsFor real numbers \(p\) and \(q\), if \(q\ne0\), what is the nature of the roots of the equation \(x^2-2px+(p^2+q^2)=0\)?Class 10Quadratic EquationsNature of RootsLevel 37ExpertMathematicsLet \(p\) and \(q\) be real numbers. If \(x^2-2px+(p^2-q^2)=0\) and \(q\neq 0\), what is the nature of the roots of this quadratic equation?Class 10Quadratic EquationsNature of RootsLevel 37ExpertMathematicsFor the equation \(3x^2-2(2k+1)x+(k+1)^2=0\) to have two distinct real roots, which condition must \(k\) satisfy?Class 10Quadratic EquationsNature of RootsLevel 37ExpertMathematicsFor the quadratic equation \(3x^2-2(2k+1)x+(k+1)^2=0\) to have equal roots, what are the values of \(k\)?Class 10Quadratic EquationsNature of RootsLevel 37ExpertMathematicsIf the equation \(x^2+2(m-2)x+(m^2-3m+4)=0\) has no real roots, what is the correct condition on \(m\)?Class 10Quadratic EquationsNature of RootsLevel 37ExpertMathematicsIf \\(x^2+2(m-2)x+(m^2-3m+4)=0\\) has equal roots, what is the value of \\(m\\)?Class 10Quadratic EquationsNature of RootsLevel 37ExpertMathematicsGiven that \\(\alpha\ne -1\\), what condition on \\(\alpha\\) is necessary for the equation \\((\alpha+1)x^2-2\alpha x+\alpha=0\\) to have real roots?Class 10Quadratic EquationsNature of RootsLevel 37ExpertMathematicsFor which values of \(\lambda\) does the equation \(x^2-2\lambda x+\lambda=0\) have equal roots?Class 10Quadratic EquationsNature of RootsLevel 37ExpertMathematicsWhich root nature is correct for 2x² − 5√2x + 12 = 0?Class 10Quadratic EquationsNature of RootsLevel 37HardMathematicsWhat is the nature of the roots of the quadratic equation \(3x^2-2\sqrt{6}x+2=0\)?Class 10Quadratic EquationsNature of RootsLevel 37ExpertMathematicsWhich quadratic equation has real and distinct roots?Class 10Quadratic EquationsNature of RootsLevel 37ExpertMathematicsIf \(a\) and \(b\) are real numbers, which of the following relations is necessary for the equation \(x^2-2(a+b)x+(a^2+b^2)=0\) to have real roots?Class 10Quadratic EquationsNature of RootsLevel 37ExpertMathematicsFor real numbers a and b, if the equation \(x^2-2(a+b)x+(a-b)^2=0\) has real and distinct roots, which condition on a and b is correct?Class 10Quadratic EquationsNature of RootsLevel 37ExpertMathematicsIf \(k\neq 0\) and \(kx^2-2(k+1)x+(k+3)=0\) is a quadratic equation, what must be the value of \(k\) for it to have equal roots?Class 10Quadratic EquationsNature of RootsLevel 37ExpertMathematicsIf \(k\) is a real number, what is the correct condition for the equation \(x^2+2(k-1)x+(k+5)=0\) to have no real roots?Class 10Quadratic EquationsNature of RootsLevel 37ExpertMathematicsFor which value of \(k\) will the two roots of the quadratic equation \(2x^2-(k+4)x+2k=0\) be equal?Class 10Quadratic EquationsNature of RootsLevel 37ExpertMathematicsFor what value of \(k\) will the quadratic equation \(2x^2-(k+4)x+2k=0\) have equal roots?Class 10Quadratic EquationsNature of RootsLevel 37ExpertMathematicsFor the equation \((p+1)x^2-2(p+2)x+(p+4)=0\), where \(p\ne -1\), what condition on \(p\) ensures that the roots are real?Class 10Quadratic EquationsNature of RootsLevel 37Expert