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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 roots of (x^2-4x-12=0), what is ((\alpha-5)(\beta-5))?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Expert MathematicsIf both roots of (x^2-6x+c=0) are real and positive, what is the correct condition on (c)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Expert MathematicsIf (\alpha,\beta) are roots of (x^2-5x-3=0), what is (\alpha^2+5\beta+\alpha\beta)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Expert MathematicsIf (\alpha,\beta) are the roots of (4x^2-12x+5=0), what is the correct value of (\alpha^3+\beta^3)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Expert MathematicsIf (\alpha,\beta) are the roots of (4x^2-12x+5=0), what is (\alpha^3+\beta^3)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Expert MathematicsIf (\alpha,\beta) are roots of (x^2-11x+30=0), what is (\frac{\alpha+1}{\alpha-1}+\frac{\beta+1}{\beta-1})?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Expert MathematicsIf (\alpha,\beta) are roots of (x^2-11x+30=0), what is the correct value of (\frac{\alpha+1}{\alpha-1}+\frac{\beta+1}{\beta-1})?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Expert MathematicsIf (\alpha,\beta) are the roots of (x^2-9x+20=0), what is (\frac{\alpha+2}{\alpha-2}+\frac{\beta+2}{\beta-2})?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Expert MathematicsFor (9x^2-6(a-1)x+a^2-4a-5=0) to have real roots, what is the correct condition on (a)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Expert MathematicsFor (16x^2-8(a-2)x+a^2-6a=0) to have real roots, what is the correct condition on (a)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Expert MathematicsIf the roots of (x^2+px+24=0) are (r) and (r+2), what are the possible values of (p)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Expert MathematicsIf (kx^2-12x+k=0) has real reciprocal roots, what is the correct condition on (k)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Expert MathematicsIf (\alpha,\beta) are the roots of (x^2-8x+2=0), what is (\frac{1}{\alpha^2}+\frac{1}{\beta^2})?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Expert MathematicsIf the roots of (3x^2+mx+10=0) are in the ratio (2:5), what are the possible values of (m)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Expert MathematicsIf (\alpha,\beta) are the roots of (x^2-7x+12=0), which equation has roots (2\alpha+3) and (2\beta+3)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Expert MathematicsIf (x^2-2(a+5)x+a^2+18=0) has equal roots, what is the value of (a)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Expert MathematicsIf the positive difference between the roots of (5x^2-16x+p=0) is (\frac{6}{5}), what is the value of (p)?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 (\alpha,\beta) are the roots of (x^2-2(a+3)x+a^2+6a+5=0), what is the positive value of (\alpha-\beta)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Expert MathematicsIf ((m-1)x^2+2(m+1)x+(m-1)=0) has real reciprocal roots, what is the correct condition on (m)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Expert