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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 the equation \(kx^2-2(k+1)x+(k+4)=0\) has equal roots, what is the value of \(k\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Hard MathematicsIf the universal set is \(U=\{x:x\in\mathbb{Z},\ 0\le x\le 10\}\) and \(A=\{x:x\in U\text{ and }x^2-5x+6=0\}\), which of the following is the complement \(A'\) of \(A\) with respect to \(U\)?Class 10SetsComplement of a Set and Its PropertiesLevel 19Medium MathematicsIf \(\alpha\) and \(\beta\) are the roots of the quadratic equation \(x^2-3x-28=0\), what is the value of \((\alpha+1)(\beta+1)\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Hard MathematicsWhich quadratic equation has real and equal roots?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Hard MathematicsIf the two roots of the equation \(x^2+kx+49=0\) are equal and negative, what is the value of \(k\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Hard MathematicsIf \(\alpha\) and \(\beta\) are the roots of the equation \(x^2-4x-5=0\), what is the value of \((\alpha+2)(\beta+2)\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Hard MathematicsIf α and β are roots of x^2 - 9x + 20 = 0, what can be the value of (α + β)/(α - β)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Hard MathematicsIf \(\alpha\) and \(\beta\) are the roots of the quadratic equation \(x^2-8x+12=0\), what is the value of \(\alpha^2\beta^2\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Hard MathematicsIf \(\alpha\) and \(\beta\) are the roots of the quadratic equation \(x^2-10x+24=0\), what is the value of \((\alpha-2)(\beta-2)\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Hard MathematicsWhich of the following is the correct pair of roots of the quadratic equation \(x^2-(2m+3)x+(m+1)(m+2)=0\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Hard MathematicsIf c(\alphac) and c(\betac) are the roots of the equation c(x^2-6x+2=0c), what is the value of c(\alpha^2+\beta^2c)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Hard MathematicsIf the roots of the equation \(x^2+px+q=0\) are \(5\) and \(-2\), what is the value of \(p-q\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Hard MathematicsIf the roots of the quadratic equation \(5x^2+px+q=0\) are \(3\) and \(-4\), what is the value of \(\frac{q}{5}\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Hard MathematicsIf \(\alpha\) and \(\beta\) are the roots of the quadratic equation \(x^2-9x+18=0\), what is the value of \((\alpha-2)(\beta-2)\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Hard MathematicsIf the two roots of the equation \(x^2-2(m+2)x+(m+2)^2=0\) are equal, which statement about \(m\) is correct?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Hard MathematicsIf the quadratic equation \(x^2-4x+(m+4)=0\) has no real roots, which condition on \(m\) is correct?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Hard MathematicsFor the quadratic equation \(ax^2+bx+c=0\), where \(a\ne0\), when will its roots be reciprocals of each other?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Hard MathematicsIf the roots of the equation \(x^2+px+18=0\) are in the ratio \(1:2\) and both roots are negative, what is the value of \(p\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Hard MathematicsIf the roots of the equation \(x^2-9x+c=0\) are in the ratio \(1:2\), what is the value of \(c\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Hard MathematicsIf α and β are roots of x² + 4x − 21 = 0, what is the value of |α − β|?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Medium