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Transformed Roots

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

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 each root of (x^2-4x-12=0) is increased by (1), which monic equation is formed from the new roots?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Hard MathematicsIf (4\alpha) and (4\beta) are new roots and (\alpha+\beta=3), what is the sum of the new roots?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Medium MathematicsIf (3\alpha) and (3\beta) are new roots and (\alpha+\beta=4), what is the sum of the new roots?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Medium MathematicsIf (2\alpha) and (2\beta) are roots and (\alpha+\beta=5), what is the sum of the new roots?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Medium