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Real Roots

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

MathematicsChoose the correct condition on (k) for real roots of (4x^2+4kx+9=0).Class 10Quadratic EquationsNature of RootsLevel 38MediumMathematicsIf the discriminant of a quadratic equation \(ax^2+bx+c=0\) with real coefficients is \(D<0\), what is the nature of its roots?Class 10Quadratic EquationsNature of RootsLevel 38MediumMathematicsIf \(a\) is a real number, what is the nature of the roots of the equation \(2x^2-4ax+(2a^2-3)=0\)?Class 10Quadratic EquationsNature of RootsLevel 37HardMathematicsIf \(p\) is any real number, what will be the nature of the roots of the equation \(x^2+2px+p^2-1=0\)?Class 10Quadratic EquationsNature of RootsLevel 37HardMathematicsIf the discriminant of a quadratic equation with real coefficients is \(D=2r^2+3\), where \(r\) is a real number, what is the correct conclusion about its roots?Class 10Quadratic EquationsNature of RootsLevel 37HardMathematicsWhat condition on \(u\) is necessary for the equation \(x^2-2ux+u^2+7u=0\) to have real roots?Class 10Quadratic EquationsNature of RootsLevel 37HardMathematicsFor which interval of (t) will the equation (x^2+2tx+t+4=0) have no real roots?Class 10Quadratic EquationsNature of RootsLevel 37HardMathematicsWhat condition on the parameter \(a\) is necessary for the equation \(x^2+2(a+1)x+a^2+3=0\) to have real roots?Class 10Quadratic EquationsNature of RootsLevel 37HardMathematicsWhich of the following quadratic equations has two real and equal roots?Class 10Quadratic EquationsNature of RootsLevel 37MediumMathematicsA student says that the equation \(x^2-2x+5=0\) has two real roots because \(b^2\) is positive. What is the correct evaluation of this statement?Class 10Quadratic EquationsNature of RootsLevel 37MediumMathematicsWhich condition on \(k\) is necessary for the quadratic equation \(3x^2+2kx+k=0\) to have real roots?Class 10Quadratic EquationsNature of RootsLevel 37MediumMathematicsIf the parabola representing a quadratic equation neither intersects nor touches the x-axis, what can be concluded about its real roots?Class 10Quadratic EquationsNature of RootsLevel 37MediumMathematicsChoose the correct statement about the nature of the roots of \(2x^2-5x+2=0\).Class 10Quadratic EquationsNature of RootsLevel 37MediumMathematicsIf the discriminant of the quadratic equation \\(ax^2+bx+c=0\\) is \\(D=b^2-4ac\\), what is the nature of its roots when \\(D>0\\)?Class 10Quadratic EquationsNature of RootsLevel 37MediumMathematicsFor the quadratic equation \\(7x^2+2x+3=0\\), the discriminant is \\(D=b^2-4ac\\). What is the value of \\(D\\)?Class 10Quadratic EquationsNature of RootsLevel 39EasyMathematicsWhat is the discriminant \(D\) of the quadratic equation \(3x^2-6x+1=0\)?Class 10Quadratic EquationsNature of RootsLevel 39EasyMathematicsStatement: If the discriminant \(D<0\), the equation has two real and distinct roots. What type of statement is this?Class 10Quadratic EquationsNature of RootsLevel 39EasyMathematicsWhich of the following quadratic equations has real, rational, and distinct roots?Class 10Quadratic EquationsNature of RootsLevel 39EasyMathematicsIf the discriminant of a quadratic equation with real coefficients is \(D=-9\), which statement about its roots is correct?Class 10Quadratic EquationsNature of RootsLevel 39EasyMathematicsWhat is the nature of the roots of the equation \(5x^2-20x+20=0\)?Class 10Quadratic EquationsNature of RootsLevel 39Easy