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Nature 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 discriminant of a quadratic equation is (D=(a-1)^2+5), where (a) is a real number, which statement correctly describes the nature of its roots?Class 10Quadratic EquationsNature of RootsLevel 38Hard MathematicsA student assumes that a quadratic equation has two real roots when its discriminant is D = -4. What is the correct conclusion?Class 10Quadratic EquationsNature of RootsLevel 38Hard MathematicsA quadratic equation with rational coefficients has discriminant D = 18. A student writes that its roots are rational. What is the correct correction?Class 10Quadratic EquationsNature of RootsLevel 38Hard MathematicsFor which interval of the parameter \(a\) does the quadratic equation \(3x^2-2(2a+1)x+(a^2+a+1)=0\) have no real roots?Class 10Quadratic EquationsNature of RootsLevel 38Hard MathematicsFor which values of \(a\) will the equation \(3x^2-2(2a+1)x+(a^2+a+1)=0\) have real and distinct roots?Class 10Quadratic EquationsNature of RootsLevel 38Hard MathematicsWhat condition on \(a\) is necessary for the equation \(3x^2-2(2a+1)x+(a^2+a+1)=0\) to have real roots?Class 10Quadratic EquationsNature of RootsLevel 38Hard MathematicsIf the equation \(x^2-2hx+h^2+8h=0\) has real and distinct roots, which condition on \(h\) is necessary?Class 10Quadratic EquationsNature of RootsLevel 38Hard MathematicsFor the quadratic equation \(x^2+2gx+g^2-6g+11=0\) to have equal roots, what should be the value of \(g\)?Class 10Quadratic EquationsNature of RootsLevel 38Hard MathematicsIf the equation \(x^2+2gx+g^2-6g+11=0\) has real roots, what condition must \(g\) satisfy?Class 10Quadratic EquationsNature of RootsLevel 38Hard MathematicsIf \(v\) is any real number, which statement correctly describes the nature of the roots of \(2x^2-4vx+2v^2+5=0\)?Class 10Quadratic EquationsNature of RootsLevel 38Hard MathematicsIf \(w\) is a real number, what is the nature of the roots of the equation \(4x^2-4wx+w^2=0\)?Class 10Quadratic EquationsNature of RootsLevel 38Hard MathematicsAssume that \(a\) and \(b\) are real numbers. Which statement about the roots of the equation \(x^2+2(a-b)x+(a+b)^2=0\) is correct?Class 10Quadratic EquationsNature of RootsLevel 38Hard MathematicsWhen will the two roots of the equation \(x^2-(m+n)x+mn=0\) be equal?Class 10Quadratic EquationsNature of RootsLevel 38Hard MathematicsIf \(a\ne b\), what is the nature of the roots of the equation \(x^2-2(a+b)x+4ab=0\)?Class 10Quadratic EquationsNature of RootsLevel 38Hard MathematicsFor the quadratic equation \(x^2-(a+6)x+6a=0\) to have equal roots, what is the value of \(a\)?Class 10Quadratic EquationsNature of RootsLevel 38Hard MathematicsIf the discriminant of a quadratic equation is \(D=(z+1)^2-9\), in which interval must \(z\) lie for the equation to have no real roots?Class 10Quadratic EquationsNature of RootsLevel 38Hard MathematicsIf the discriminant of a quadratic equation is \(D=(s-2)(s+5)\), where \(s\) is real, when will its roots be real and distinct?Class 10Quadratic EquationsNature of RootsLevel 38Hard MathematicsWhat is the nature of roots of (x^2+2(3u+1)x+9u^2-6u+5=0)?Class 10Quadratic EquationsNature of RootsLevel 38Hard MathematicsWhat is the correct statement about the real roots of x² + 2(2y−1)x + 4y² + 3 = 0?Class 10Quadratic EquationsNature of RootsLevel 38Hard MathematicsIf the equation \(x^2-2\sqrt{n}x+4=0\) has real and equal roots, what is the value of \(n\)?Class 10Quadratic EquationsNature of RootsLevel 38Hard