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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 product of the roots of the equation \(x^2-2(a-3)x+a^2-16=0\) is zero, what are the values of \(a\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Expert MathematicsIf one root of (2x^2-(3p+2)x+p(p+2)=0) is (p), what will be the other root?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Hard 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^2-7x+k=0) are reciprocals of each other, what is the value of (k)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Hard 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 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 2 is subtracted from each root of the equation \(x^2-6x-16=0\), what is the product of the resulting roots?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Hard MathematicsIf 3 and 5 are the roots of the equation \(ax^2+bx+15=0\), what is the value of \(a\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Hard 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 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 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 roots of the quadratic equation \(x^2+6x+k=0\) are \(-2\) and \(-4\), what is the value of \(k\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Hard MathematicsIf 2 and 3 are the roots of the equation \(ax^2+bx+6=0\), what is the value of \(a\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Hard MathematicsIf (alpha+beta=-7) and (alphabeta=-18), which monic quadratic equation has alpha and beta as its roots?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Medium MathematicsIf the roots of a quadratic equation \(ax^2+bx+d=0\) are \(c\) and \(-c\), what is the value of the ratio \(\frac{d}{a}\) of the constant term to the leading coefficient?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Medium MathematicsIf α and β are roots of 6x² + 5x − 4 = 0, what is αβ?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Medium MathematicsOne root of the equation \(x^2-17x+70=0\) is 7. What is the other root?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Medium MathematicsWhat is the product of the roots of the equation \(7x^2+4x-9=0\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Medium MathematicsFor the quadratic equation \(x^2-18x+81=0\), what are the sum and product of its roots, respectively?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Medium MathematicsIf the roots of a quadratic equation are \(b\) and \(-b\), what is the value of the ratio \(\frac{c}{a}\) of its constant term \(c\) to its leading coefficient \(a\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Medium