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Sum And Product Of Roots

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

MathematicsIf the sum of the roots of a quadratic equation is 7 and their product is 10, which is its monic quadratic equation?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Expert MathematicsIf \(\alpha\) and \(\beta\) are the roots of the equation \(x^2+8x+12=0\), what is the value of \((\alpha-\beta)^2+3\alpha\beta\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Expert MathematicsWhat are the roots of the equation \(x^2-(u-v)x-uv=0\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Expert 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 MathematicsIf \(\alpha\) and \(\beta\) are the roots of the equation \(x^2-8x+12=0\), what is the value of \((\alpha+2)(\beta+2)\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Hard MathematicsIf calphac and cbetac are the roots of cx^2-7x+10=0c, what is the value of (alpha-1)(beta-1)c?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Hard MathematicsIf (alpha) and (beta) are the roots of (x^2-9x+20=0), what is the value of (alpha+beta+alphabeta)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Medium MathematicsIf 8\alpha+\beta=-59 and 8\alpha\beta=-149, which monic quadratic equation has 8\alpha9 and 8\beta9 as its roots?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Medium MathematicsIf the sum of the roots of a quadratic equation is 9 and their product is 18, which monic quadratic equation is formed?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Medium MathematicsIf the sum of the roots of a monic quadratic equation is 5 and their product is 6, which of the following equations can have those roots?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Medium MathematicsIf (alpha+beta=-3) and (alphabeta=-10), which monic quadratic equation has (alpha) and (beta) as its roots?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Medium MathematicsWhich monic quadratic equation has a sum of roots equal to 7 and a product of roots equal to 10?Class 10Quadratic EquationsIntroduction to Quadratic EquationsLevel 29Hard MathematicsIf the roots of \(x^2+rx+36=0\) are 6 and 6, what is the value of \(r\)?Class 10Quadratic EquationsIntroduction to Quadratic EquationsLevel 29Medium MathematicsIf the zeros of \(f(x)=x^2+px+q\) are \(7+\sqrt{13}\) and \(7-\sqrt{13}\), what is the value of \(p+q\)?Class 10PolynomialsIrrational numbers and real numbersLevel 26Hard