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Quadratic Equations

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

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 MathematicsIf the roots of the quadratic equation \(x^2-10x+k=0\) are distinct prime numbers, what is the value of \(k\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Hard MathematicsWhich statement is always true about x^2-(a+3)x+3a=0?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Medium MathematicsIf \(\alpha\) and \(\beta\) are the roots of the equation \(x^2-5x+1=0\), what is the value of \(\alpha^2+\beta^2\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Hard MathematicsFor the equation \(x^2-2(k+1)x+k^2=0\) to have real and distinct roots, what is the correct condition on \(k\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Hard MathematicsIf α and β are roots of x^2+px+q=0 and α+1 and β+1 are roots of x^2-5x+6=0, what are p and q?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Hard MathematicsIf the quadratic equation \(x^2+kx+16=0\) has equal roots, what are the possible values of \(k\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Hard MathematicsFor the equation \(x^2-2x+(p+3)=0\) to have no real roots, what is the correct condition on \(p\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Hard MathematicsFor the general quadratic equation ax^2+bx+c=0, which relation is correct when the roots are equal?Class 10Quadratic EquationsNature of RootsLevel 33Medium MathematicsIf the difference between the roots of the equation \(x^2-(k+2)x+2k=0\) is 2, find the values of \(k\).Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Hard MathematicsIf the quadratic equation \(2x^2+\lambda x+8=0\) has equal roots, what can be the values of \(\lambda\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Hard MathematicsIf \(x=2\) is a root of the equation \(kx^2-6x+4=0\), what is the value of \(k\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Hard MathematicsWhich statement is correct about the roots of the equation \(5x^2-2x+1=0\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Hard MathematicsIf the two roots of the quadratic equation \(x^2+bx+c=0\) are opposites of each other, which of the following conditions is necessary?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Hard MathematicsWhen will the real roots of the quadratic equation \(ax^2+bx+c=0\), where \(a\ne0\), be additive inverses of each other?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Hard MathematicsThe roots of x^2-5x+6=0 are α and β. Which equation has roots α+1 and β+1?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Hard MathematicsIf the quadratic equation \(x^2+2(k-1)x+k+5=0\) has equal roots, what are the possible values of \(k\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Hard MathematicsThe roots of x^2-px+36=0 are positive integers and their difference is 5. What is p?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Medium MathematicsWhat is the correct condition on \(a\) for the equation \(x^2-2(a+1)x+a^2+3=0\) to have real roots?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 33Hard