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Roots Of Quadratic Equation

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

MathematicsIf one root of the equation \(4x^2-(4h+1)x+h=0\) is \(\frac{1}{4}\), what is the other root?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Expert MathematicsIf the roots of the equation \(x^2-16x+q=0\) are in the ratio \(5:3\), what is the value of \(q\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Expert MathematicsIf one root of \(x^2-(m+9)x+9m=0\) is \(9\), what is the other root?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Expert MathematicsIf the roots of the quadratic equation \(x^2+ax+b=0\) are \(4+\sqrt{7}\) and \(4-\sqrt{7}\), what is the value of \(a+b\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Expert 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 MathematicsIf both roots of the equation \(x^2-12x+m=0\) are prime numbers, what is the value of \(m\)?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 the roots of the equation x² − 14x + q = 0 are in the ratio 3:4, what is the value of q?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Expert MathematicsIf \(\alpha\) and \(\beta\) are the roots of the equation \(x^2-8x+n=0\) and \(\alpha^2+\beta^2=40\), what is the value of \(n\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Expert MathematicsIf the product of the roots of the equation \(x^2-2(a-2)x+a^2-9=0\) is zero, what are the values of \(a\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Expert MathematicsIf the roots of the quadratic equation \(x^2+ax+b=0\) are \(3+\sqrt{2}\) and \(3-\sqrt{2}\), what is the value of \(a+b\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Expert MathematicsIf \(\alpha\) and \(\beta\) are the roots of the equation \(x^2-7x+12=0\), what is the value of \(\frac{\alpha+1}{\alpha-1}+\frac{\beta+1}{\beta-1}\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 32Expert MathematicsIf the roots of the equation \(x^2-(2a+3)x+(a^2+3a+2)=0\) are consecutive integers, what are the roots?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Expert MathematicsIf (alpha,beta) are the roots of (x^2-6x+n=0) and (alpha^2+beta^2=20), what is the value of (n)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Expert MathematicsIf the roots of \(x^2+ax+b=0\) are \(\frac{1}{2+\sqrt{3}}\) and \(\frac{1}{2-\sqrt{3}}\), what is the value of \(a\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Expert MathematicsIf the roots of the quadratic equation \(x^2-2x+k=0\) are \(\tan\theta\) and \(\cot\theta\), what is the value of \(k\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Expert MathematicsIf the roots of the equation \(x^2+ax+b=0\) are \(2+\sqrt{3}\) and \(2-\sqrt{3}\), what is the value of \(a+b\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Expert MathematicsWhat are the two roots of the equation \(4x^2-4x+1=0\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Hard MathematicsThe difference between the two roots of the equation \(x^2+6x+r=0\) is \(2\sqrt{5}\). What is the value of \(r\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Hard MathematicsIf the roots of the quadratic equation \(x^2-(m+1)x+m=0\) are reciprocals of each other, what is the value of \(m\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Hard