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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 \(\alpha^2\beta^2\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Hard MathematicsWhich of the following quadratic equations has real and distinct roots that are irrational?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Hard MathematicsWhich pair gives the roots of the equation \(x^2-(2m+1)x+m(m+1)=0\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Hard MathematicsIf alpha and beta are the roots of the equation x^2-4x+1=0, what is the value of alpha^2+beta^2?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Hard MathematicsIf the roots of the quadratic equation \(x^2+px+q=0\) are \(4\) and \(-1\), what is the value of \(p-q\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Hard MathematicsIf 2 and −3 are the roots of the equation \(3x^2+px+q=0\), what is the value of \(\frac{q}{3}\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Hard MathematicsIf the two roots of the quadratic equation \(x^2-2(m+1)x+(m^2+2m)=0\) are equal, what is the value of \(m\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Hard MathematicsIf the equation \(x^2-2x+(m+1)=0\) has no real roots, which condition on \(m\) is correct?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Hard MathematicsIf the two roots of the quadratic equation \(x^2+bx+9=0\) are equal and positive, what is the value of \(b\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Hard MathematicsIf the roots of x² + px + 12 = 0 are in the ratio 1:3 and both are negative, what is p?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Hard MathematicsIf the roots of (x^2-6x+c=0) are in the ratio (1:2), what is the value of (c)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Hard MathematicsFor the quadratic equation \(ax^2+bx+c=0\) with integer coefficients, where \(a\ne0\), which condition ensures that both roots are distinct real irrational numbers? Here, the discriminant is \(\Delta=b^2-4ac\).Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Hard MathematicsIf \(\alpha\) and \(\beta\) are the roots of the equation \(x^2-10x+25=0\), what is the value of \(\alpha-\beta\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Hard MathematicsIf \(\alpha\) and \(\beta\) are the roots of the equation \(x^2-5x+4=0\), what is the sum of \((\alpha+2)\) and \((\beta+2)\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Hard MathematicsIf α and β are roots of x² − 3x + 2 = 0, which equation has 2α and 2β as roots?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Hard MathematicsIf 1 is subtracted from each root of the equation \(x^2-4x-12=0\), what is the product of the resulting roots?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Hard MathematicsIf the difference of roots of (x^2-5x+q=0) is (1), what is the value of (q)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Hard MathematicsIf the roots of x² − (a + 1)x + a = 0 are 1 and a, why is this correct?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Hard MathematicsHow many real roots does the equation \(x^2+2x+5=0\) have?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Hard MathematicsIf the quadratic equation \(kx^2-6x+9=0\) has equal roots and \(k\ne0\), what is the value of \(k\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Hard