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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।

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 \(x^2-(2a+5)x+(a+2)(a+3)=0\), where \(a\) is a real constant, what will be the nature of its roots?Class 10Quadratic EquationsNature of RootsLevel 39Expert 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 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 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 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 MathematicsThe equation \(x^2-2(4t+1)x+(7t^2+2t+5)=0\) has no real roots. Which is the correct interval for \(t\)?Class 10Quadratic EquationsNature of RootsLevel 39Expert MathematicsIf (\alpha\neq-3) in ((\alpha+3)x^2-2\alpha x+(\alpha-2)=0), what is the condition on (\alpha) for real roots?Class 10Quadratic EquationsNature of RootsLevel 39Expert MathematicsIf \(a\) and \(b\) are real numbers, which condition is necessary and sufficient for the equation \(x^2-2(a-2b)x+(a+2b)^2=0\) to have real roots?Class 10Quadratic EquationsNature of RootsLevel 39Expert MathematicsIf \(a\) and \(b\) are real numbers and the roots of \(x^2-2(a+b)x+3ab=0\) are real, which statement about \(a\) and \(b\) is correct?Class 10Quadratic EquationsNature of RootsLevel 39Expert MathematicsFor which values of \(k\) will the quadratic equation \(x^2-2(k+1)x+(k^2+1)=0\) have two distinct real roots?Class 10Quadratic EquationsNature of RootsLevel 38Expert 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 MathematicsA geometric situation leads to the quadratic equation \(L^2-2(a+4)L+(a^2+6a+13)=0\). What condition on \(a\) is necessary for \(L\) to have real values?Class 10Quadratic EquationsNature of RootsLevel 38Expert MathematicsHow many points of intersection are there between the parabola \(y=x^2-2kx+k^2+4\) and the x-axis?Class 10Quadratic EquationsNature of RootsLevel 38Expert MathematicsFor the equation \(x^2-2rx+(r^2+25)=0\), where \(r\) is any real number, what is the correct conclusion about the nature of its roots?Class 10Quadratic EquationsNature of RootsLevel 38Expert MathematicsIf the discriminant of a quadratic equation is \(D=(z-4)(z+6)\), which interval of \(z\) results in no real roots of the equation?Class 10Quadratic EquationsNature of RootsLevel 38Expert MathematicsIf \(x^2-2px+(p^2+16)=0\), what will be the nature of its roots for any real value of \(p\)?Class 10Quadratic EquationsNature of RootsLevel 38Expert MathematicsIf (\alpha\neq-2) in ((\alpha+2)x^2-2\alpha x+(\alpha-1)=0), what is the condition on (\alpha) for real roots?Class 10Quadratic EquationsNature of RootsLevel 38Expert MathematicsIf a and b are real numbers, which is the correct condition for the equation \(x^2-2(a-b)x+(a+b)^2=0\) to have real roots?Class 10Quadratic EquationsNature of RootsLevel 38Expert MathematicsIf (x^2-2(a+b)x+2ab=0) has real roots, which statement is always true for (a) and (b)?Class 10Quadratic EquationsNature of RootsLevel 38Expert