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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।

MathematicsWhat is the nature of the roots of the quadratic equation \(3x^2-2\sqrt{15}x+5=0\)?Class 10Quadratic EquationsNature of RootsLevel 38Hard MathematicsWhat condition on \(c\) is necessary for the quadratic equation \(x^2-2(c+1)x+c^2-2c+5=0\) to have real roots?Class 10Quadratic EquationsNature of RootsLevel 38Hard MathematicsFor a real parameter \(t\), which value of \(t\) will make the equation \((t-1)x^2-2(t+2)x+(t+5)=0\) have equal roots?Class 10Quadratic EquationsNature of RootsLevel 38Hard MathematicsFor which value of k will (k+3)x² + 2kx + (k−1) = 0 have equal roots?Class 10Quadratic EquationsNature of RootsLevel 38Hard MathematicsWhich value of \(q\) is required for the two roots of the quadratic equation \(2x^2-(q+4)x+2q=0\) to be equal?Class 10Quadratic EquationsNature of RootsLevel 38Hard MathematicsWhat condition on \(a\) is required for the equation \(x^2+2(a+3)x+a^2+10a+17=0\) to have no real roots?Class 10Quadratic EquationsNature of RootsLevel 38Hard MathematicsIf m is a real number, when will the roots of \(x^2-2(m-4)x+m^2-16=0\) be real and distinct?Class 10Quadratic EquationsNature of RootsLevel 38Hard MathematicsFor the equation \\((r+2)x^2-2(r+5)x+(r+2)=0\\), what is the value of \(r\) for which the roots are real and equal?Class 10Quadratic EquationsNature of RootsLevel 38Hard MathematicsWhat is the nature of the roots of the quadratic equation \(x^2-13x+40=0\)?Class 10Quadratic EquationsNature of RootsLevel 38Medium MathematicsWhat is the nature of the roots of the equation \(4x^2-12x+11=0\)?Class 10Quadratic EquationsNature of RootsLevel 38Medium MathematicsChoose the correct statement about the nature of the roots of \\(x^2+8x+18=0\\).Class 10Quadratic EquationsNature of RootsLevel 38Medium MathematicsA number-related problem leads to the equation \(n^2-15n+56=0\). What is the nature of the roots of this quadratic equation?Class 10Quadratic EquationsNature of RootsLevel 38Medium MathematicsAn area-based problem leads to the equation \(s^2-6s+10=0\). What is the correct conclusion about the real values of \(s\)?Class 10Quadratic EquationsNature of RootsLevel 38Medium MathematicsFor the quadratic equation \(2x^2-5x+q=0\) to have two real and equal roots, what should be the value of \(q\)?Class 10Quadratic EquationsNature of RootsLevel 38Medium MathematicsFor which values of \\(k\\) will the equation \\(x^2-2(k-3)x+16=0\\) have equal roots?Class 10Quadratic EquationsNature of RootsLevel 38Medium MathematicsFor a quadratic equation \(ax^2+bx+c=0\), where \(a,b,c\) are rational numbers and \(a\ne0\), if the discriminant \(D=b^2-4ac=100\), which statement correctly describes the 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 MathematicsWhat is the nature of the roots of the equation \(7x^2-9x+2=0\)?Class 10Quadratic EquationsNature of RootsLevel 38Medium MathematicsWhat is the nature of the roots of \\(2x^2+x+2=0\\)?Class 10Quadratic EquationsNature of RootsLevel 38Medium MathematicsWhat is the discriminant of \\(x^2+9x+14=0\\), and what is the nature of its roots?Class 10Quadratic EquationsNature of RootsLevel 38Medium