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Quadratic Roots

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

MathematicsIf (\alpha,\beta) are the roots of (x^2-4x-2=0), what is (\alpha^2+4\beta+\alpha\beta)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Expert MathematicsIf (\alpha,\beta) are the roots of (3x^2-8x+4=0), what is (\alpha^3+\beta^3)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Expert MathematicsIf the roots of (x^2+px+15=0) are (r) and (r+2), what are the possible values of (p)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Expert MathematicsIf (kx^2-10x+k=0) has real reciprocal roots, which condition on (k) is correct?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Expert MathematicsIf (\alpha,\beta) are the roots of (x^2-6x+3=0), what is (\frac{1}{\alpha^2}+\frac{1}{\beta^2})?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Expert MathematicsWhich statement is always true for (x^2-(a+6)x+6a=0)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Hard MathematicsIf (\alpha,\beta) are the roots of (x^2-9x+14=0), which equation has roots (\alpha-3) and (\beta-3)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Expert MathematicsIf the positive difference between the roots of (4x^2-12x+m=0) is (1), what is the value of (m)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Expert MathematicsIf (\alpha,\beta) are the roots of (x^2-(2r+5)x+(r^2+5r+6)=0), what is the positive value of (\alpha-\beta)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Expert MathematicsIf (\alpha,\beta) are roots of (x^2+x-1=0), what is (\alpha^5+\beta^5)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Expert MathematicsIf (x^2+bx+25=0) has equal and negative roots, what is the value of (b)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Expert MathematicsIf (\alpha,\beta) are roots of (x^2-4x+c=0) and (\alpha^2+\beta^2=10), what are the roots of the equation?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Expert MathematicsIf one root of (2x^2-(h+1)x+h=0) is always (\frac{1}{2}), what is the other root?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Expert MathematicsIf the roots of the quadratic equation \(x^2+px+q=0\) are \(-2\) and \(5\), what is the value of \(p-q\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Expert MathematicsIf (\alpha,\beta) are roots of (x^2-5x+6=0), what is the correct value of (\alpha^2-4\alpha+\beta^2-4\beta)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Expert MathematicsIf (\alpha,\beta) are roots of (x^2-5x+6=0), what is (\alpha^2-4\alpha+\beta^2-4\beta)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Expert MathematicsFor (x^2+2x+\lambda=0) to have real distinct roots and both negative roots, what is the correct condition on (\lambda)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Expert MathematicsIf (\alpha,\beta) are roots of (2x^2-7x+3=0), what is the positive value of (\alpha-\beta)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Expert MathematicsIf (x^2+px+16=0) has equal and positive roots, what is the value of (p)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Expert MathematicsIf both roots of (x^2-10x+m=0) are prime numbers, what is the sum of possible values of (m)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Expert