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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 (\alpha\neq-3) in ((\alpha+3)x^2-2\alpha x+(\alpha-2)=0), what is the condition on (\alpha) for real roots?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 MathematicsIf (x^2+2(v+2)x+(4v+11)=0) has no real roots, in which interval will (v) lie?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 MathematicsWhich condition is required for the equation \(x^2-(t+7)x+7t=0\) to have two real and distinct roots?Class 10Quadratic EquationsNature of RootsLevel 39Expert MathematicsIf x² − 2(k − 4)x + (k² − 10k + 27) = 0 has no real roots, which condition on k is correct?Class 10Quadratic EquationsNature of RootsLevel 39Hard MathematicsFor a quadratic equation \(ax^2+bx+c=0\) with real coefficients, where \(a\ne0\), which condition identifies that its roots have opposite signs?Class 10Quadratic EquationsNature of RootsLevel 39Expert MathematicsWhat is the nature of the roots of the equation \(3x^2-2\sqrt{21}x+7=0\)?Class 10Quadratic EquationsNature of RootsLevel 39Expert MathematicsChoose the correct conclusion about the nature of the roots of \(2x^2-5\sqrt{2}x+8=0\).Class 10Quadratic EquationsNature of RootsLevel 39Expert MathematicsWhat is the nature of the roots of the equation \(6x^2-4\sqrt{6}x+4=0\)?Class 10Quadratic EquationsNature of RootsLevel 39Expert