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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 \(\alpha\) and \(\beta\) are the roots of the equation \(x^2+6x+8=0\), what is the value of \((\alpha-\beta)^2+2\alpha\beta\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Expert MathematicsIf the roots of the equation \(x^2-(2a+3)x+(a^2+3a+2)=0\) are consecutive integers, what are the roots?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Expert MathematicsWhat are the roots of the quadratic equation \(x^2-(a+b)x+ab=0\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Expert MathematicsIf the two roots of the quadratic equation \(ax^2+bx+c=0\), where \(a\ne0\), are reciprocals of each other, which relation among the coefficients is necessary?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Expert MathematicsIf (alpha,beta) are the roots of (x^2-6x+n=0) and (alpha^2+beta^2=20), what is the value of (n)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Expert MathematicsIf the product of the roots of the equation \(x^2-2(a+1)x+a^2-1=0\) is zero, which values of \(a\) are possible?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Expert MathematicsIf the roots of \(x^2+ax+b=0\) are \(\frac{1}{2+\sqrt{3}}\) and \(\frac{1}{2-\sqrt{3}}\), what is the value of \(a\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Expert MathematicsIf the roots of the quadratic equation \(x^2-2x+k=0\) are \(\tan\theta\) and \(\cot\theta\), what is the value of \(k\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Expert MathematicsWhat is the correct conclusion about the roots of (x^2-(2a+1)x+a(a+1)=0)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Hard MathematicsWhich statement is correct about the roots of x^2-2px+p^2-9=0?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Hard MathematicsIf the roots of the equation \(x^2+ax+b=0\) are \(2+\sqrt{3}\) and \(2-\sqrt{3}\), what is the value of \(a+b\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Expert MathematicsIf the two roots of the quadratic equation \(x^2+(m-5)x+9=0\) are equal and not of opposite signs, what are the possible values of \(m\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Expert MathematicsFor the equation \(4x^2-4(a-1)x+a^2-4a=0\) to have real roots, what is the correct condition on \(a\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Expert MathematicsIf the roots of (x^2+px+12=0) are (r) and (r+1), what are the possible values of (p)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Expert MathematicsWhich statement is always true for x^2-(a+4)x+4a=0?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Hard MathematicsIf α and β are the roots of x² − 6x + 5 = 0, which equation has roots 3α − 2 and 3β − 2?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Hard MathematicsIf ((k-2)x^2+4x+1=0) has equal roots, what is the value of (k)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Hard MathematicsWhich is the correct pair of roots of x^2+3x-18=0?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Medium MathematicsWhat are the two roots of the equation \(4x^2-4x+1=0\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Hard MathematicsIf \(x=0\) is a root of the quadratic equation \(ax^2+bx+c=0\), where \(a\ne0\), which of the following conditions must be true?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Hard