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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 \(D=(r-2)^2-9\), which interval of \(r\) results in no real roots?Class 10Quadratic EquationsNature of RootsLevel 39Expert MathematicsIf \\(m+4)x^2-2(m+2)x+m=0\\) with \\(m\ne -4\\), what will be the nature of its roots?Class 10Quadratic EquationsNature of RootsLevel 39Expert MathematicsIf the equation x² − 2(a + 1)x + (a² + 4a + 5) = 0 has no real roots, which condition on a is correct?Class 10Quadratic EquationsNature of RootsLevel 39Expert MathematicsIf x² − (a + b + 1)x + ab + a + b = 0, on what does the nature of the roots depend for a and b?Class 10Quadratic EquationsNature of RootsLevel 39Hard MathematicsIf \(x^2-(2a+5)x+(a+2)(a+3)=0\), where \(a\) is a real constant, what will be the nature of its roots?Class 10Quadratic EquationsNature of RootsLevel 39Expert MathematicsA number problem leads to the equation \(n^2-2pn+(p^2-11p)=0\). What condition on \(p\) is necessary for the equation to have two real and distinct values of \(n\)?Class 10Quadratic EquationsNature of RootsLevel 39Expert MathematicsSuppose the quadratic equation \(ax^2+bx+c=0\) has two distinct real roots. Which condition definitely indicates that the roots have opposite signs?Class 10Quadratic EquationsNature of RootsLevel 39Expert MathematicsFor the quadratic equation \(ax^2+bx+c=0\) with real coefficients, where \(a\ne0\), if \(\frac{c}{a}<0\), which statement about its roots is correct?Class 10Quadratic EquationsNature of RootsLevel 39Expert MathematicsFor the parabola \(y=x^2-2kx+(k^2-16)\), at how many distinct points will it intersect the \(x\)-axis?Class 10Quadratic EquationsNature of RootsLevel 39Expert MathematicsHow does the parabola \(y=x^2-2(k+2)x+(k+2)^2\) meet the \(x\)-axis?Class 10Quadratic EquationsNature of RootsLevel 39Expert MathematicsHow many points of intersection are there between the parabola \(y=x^2-2kx+k^2+9\) and the \(x\)-axis?Class 10Quadratic EquationsNature of RootsLevel 39Expert MathematicsIf \(r\) is any real number in the equation \(x^2-2rx+(r^2+49)=0\), what is the correct conclusion about its roots?Class 10Quadratic EquationsNature of RootsLevel 39Expert MathematicsIf \(x^2-2rx+(r^2-81)=0\) is a quadratic equation and \(r\) is any real number, what will be the nature of its roots?Class 10Quadratic EquationsNature of RootsLevel 39Expert MathematicsWhat is the nature of the roots of the equation \(x^2-2(3+\sqrt{5})x+(14+6\sqrt{5})=0\)?Class 10Quadratic EquationsNature of RootsLevel 39Expert MathematicsWhat is the nature of the roots of \\(x^2+2(3-\sqrt{10})x+16=0\\)?Class 10Quadratic EquationsNature of RootsLevel 39Expert MathematicsIf a quadratic equation has discriminant D = 49 − 16h², what are the values of h for equal roots?Class 10Quadratic EquationsNature of RootsLevel 39Medium MathematicsIf the discriminant of a quadratic equation is \(D=20n-80\), what condition on \(n\) is required for the equation to have two real and distinct roots?Class 10Quadratic EquationsNature of RootsLevel 39Expert MathematicsIf the discriminant of a quadratic equation is D = (z − 9)(z + 1), which interval of z is required for the equation to have no real roots?Class 10Quadratic EquationsNature of RootsLevel 39Expert MathematicsIf the discriminant of a quadratic equation is \(D=(m-8)^2\), what must be the value of \(m\) for the equation to have equal roots?Class 10Quadratic EquationsNature of RootsLevel 39Expert MathematicsIf the two possible values of the discriminant of a quadratic equation are \\(D_1=(y+5)^2\\) and \\(D_2=-(y+5)^2\\), with \\(y\neq -5\\), which case gives two distinct real roots?Class 10Quadratic EquationsNature of RootsLevel 39Expert