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Irrational Roots

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

MathematicsThe hypotenuse of a right triangle is 109 cm. One leg is 19 cm longer than the other leg. What is the length of the shorter leg?Class 10Quadratic EquationsWord Problems and ApplicationsLevel 41Hard MathematicsIf \(a,b,c\) are integers and \(a\ne0\), which condition identifies that the quadratic equation \(ax^2+bx+c=0\) has two distinct irrational real roots?Class 10Quadratic EquationsNature of RootsLevel 38Expert MathematicsWhich of the following equations has real, irrational, and distinct roots?Class 10Quadratic EquationsNature of RootsLevel 37Expert MathematicsIf (D=18) is the discriminant of a quadratic equation, what is the correct statement about its roots?Class 10Quadratic EquationsNature of RootsLevel 39Hard MathematicsChoose the correct nature of roots of (x^2-4x+1=0).Class 10Quadratic EquationsNature of RootsLevel 39Hard MathematicsWhat will be the nature of roots of (7x^2-5x-3=0)?Class 10Quadratic EquationsNature of RootsLevel 39Medium MathematicsWhat will be the nature of roots of (4x^2-5x-2=0)?Class 10Quadratic EquationsNature of RootsLevel 39Medium MathematicsIf (D_1=64), (D_2=15), (D_3=0), and (D_4=-9), which one gives irrational distinct roots?Class 10Quadratic EquationsNature of RootsLevel 39Medium MathematicsWhat is the nature of the roots of the equation \(2x^2-7x+1=0\)?Class 10Quadratic EquationsNature of RootsLevel 39Medium MathematicsIf the parabola of a quadratic equation with rational coefficients cuts the x-axis at two distinct points and its discriminant \(D\) is not a perfect square, what will be the nature of its roots?Class 10Quadratic EquationsNature of RootsLevel 39Medium MathematicsIf a quadratic equation with rational coefficients has discriminant \(\Delta=27\), what is the nature of its roots?Class 10Quadratic EquationsNature of RootsLevel 39Medium MathematicsWhat is the nature of the roots of the equation \(3x^2-2x-2=0\)?Class 10Quadratic EquationsNature of RootsLevel 39Medium MathematicsWhat is the nature of the roots of \(x^2-x-1=0\)?Class 10Quadratic EquationsNature of RootsLevel 39Medium 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 MathematicsWhat will be the nature of roots of (3x^2-4x-1=0)?Class 10Quadratic EquationsNature of RootsLevel 38Medium MathematicsIf (D_1=36), (D_2=11), (D_3=0), and (D_4=-5), which one gives irrational distinct roots?Class 10Quadratic EquationsNature of RootsLevel 38Medium MathematicsWhat is the nature of the roots of the equation \(x^2-3x-1=0\)?Class 10Quadratic EquationsNature of RootsLevel 38Medium MathematicsIf the discriminant of a quadratic equation is \(D=18\), what is the nature of its roots?Class 10Quadratic EquationsNature of RootsLevel 38Medium MathematicsWhat is the nature of the roots of x² − 7x + 11 = 0?Class 10Quadratic EquationsNature of RootsLevel 38Medium MathematicsWhat is the nature of the roots of the equation \(x^2-5x+3=0\)?Class 10Quadratic EquationsNature of RootsLevel 38Medium