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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 p ≠ 1 in (p − 1)x² − 2(p + 1)x + (p + 3) = 0, what is the condition on p for real roots?Class 10Quadratic EquationsNature of RootsLevel 38HardMathematicsIf a and b are real numbers, a \(\neq\) b, and \(x^2-(a+b)x+ab=0\), what will be the nature of the roots of this quadratic equation?Class 10Quadratic EquationsNature of RootsLevel 37ExpertMathematicsIf \\(x^2-(2a+1)x+a(a+1)=0\\), where \\(a\\) is a real parameter, what will be the nature of its roots?Class 10Quadratic EquationsNature of RootsLevel 37ExpertMathematicsA number puzzle gives the equation \(n^2-2pn+(p^2-5p)=0\). What condition on \(p\) is necessary for the equation to have two real and distinct values of \(n\)?Class 10Quadratic EquationsNature of RootsLevel 37ExpertMathematicsAn area situation gives l² - 2(a + 3)l + (a² + 10) = 0. What is the condition on a for real length values?Class 10Quadratic EquationsNature of RootsLevel 37HardMathematicsFor a real constant \(k\), how many points of intersection are there between the parabola \(y=x^2-2kx+k^2+1\) and the \(x\)-axis?Class 10Quadratic EquationsNature of RootsLevel 37ExpertMathematicsIf the discriminant of a quadratic equation is \(D=8m-24\), what condition on \(m\) is necessary for the equation to have real roots?Class 10Quadratic EquationsNature of RootsLevel 37ExpertMathematicsWhich quadratic equation will have two distinct real roots?Class 10Quadratic EquationsNature of RootsLevel 37ExpertMathematicsWhich of the following equations has real, irrational, and distinct roots?Class 10Quadratic EquationsNature of RootsLevel 37ExpertMathematicsWhich of the following quadratic equations has equal roots?Class 10Quadratic EquationsNature of RootsLevel 37ExpertMathematicsLet \(p\) and \(q\) be real numbers. If \(x^2-2px+(p^2-q^2)=0\) and \(q\neq 0\), what is the nature of the roots of this quadratic equation?Class 10Quadratic EquationsNature of RootsLevel 37ExpertMathematicsFor the equation \(3x^2-2(2k+1)x+(k+1)^2=0\) to have two distinct real roots, which condition must \(k\) satisfy?Class 10Quadratic EquationsNature of RootsLevel 37ExpertMathematicsGiven that \\(\alpha\ne -1\\), what condition on \\(\alpha\\) is necessary for the equation \\((\alpha+1)x^2-2\alpha x+\alpha=0\\) to have real roots?Class 10Quadratic EquationsNature of RootsLevel 37ExpertMathematicsIf \(a\) and \(b\) are real numbers, which of the following relations is necessary for the equation \(x^2-2(a+b)x+(a^2+b^2)=0\) to have real roots?Class 10Quadratic EquationsNature of RootsLevel 37ExpertMathematicsWhich condition is correct for real roots of ((k-2)x^2+2kx+(k+3)=0), if (k\neq2)?Class 10Quadratic EquationsNature of RootsLevel 37ExpertMathematicsIn ((k-2)x^2+2kx+(k+3)=0), with (k\neq2), what is the correct condition for real roots?Class 10Quadratic EquationsNature of RootsLevel 37ExpertMathematicsFor the equation \((p+1)x^2-2(p+2)x+(p+4)=0\), where \(p\ne -1\), what condition on \(p\) ensures that the roots are real?Class 10Quadratic EquationsNature of RootsLevel 37ExpertMathematicsIf \(k\) is a real number and the roots of the equation \(x^2-2(k+1)x+(k^2+4)=0\) are real, what is the correct condition on \(k\)?Class 10Quadratic EquationsNature of RootsLevel 37ExpertMathematicsWhat is the nature of the roots of the quadratic equation \(3x^2-5x+2=0\)?Class 10Quadratic EquationsNature of RootsLevel 39HardMathematicsAn area-based problem leads to the equation \(r^2-10r+30=0\). What is the correct conclusion about the real values of \(r\)?Class 10Quadratic EquationsNature of RootsLevel 39Medium