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Quadratic Equations

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

MathematicsIf x² - 2rx + (r² - 16) = 0, what is the nature of the roots for any real value of r?Class 10Quadratic EquationsNature of RootsLevel 37Medium MathematicsWhat is the nature of the roots of \\(x^2-2(3+\sqrt{2})x+(17+12\sqrt{2})=0\\)?Class 10Quadratic EquationsNature of RootsLevel 37Expert MathematicsWhat is the nature of the roots of the equation \(x^2+2(1-\sqrt{3})x+4=0\)?Class 10Quadratic EquationsNature of RootsLevel 37Expert MathematicsIf a quadratic has discriminant D = 25 - 4q², what are the values of q for equal roots?Class 10Quadratic EquationsNature of RootsLevel 37Medium MathematicsIf 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 37Expert MathematicsIf the discriminant of a quadratic equation is \(D=(u+1)(u-5)\), which interval of \(u\) results in no real roots?Class 10Quadratic EquationsNature of RootsLevel 37Expert MathematicsThe discriminant of a quadratic equation is D = (s − 2)^2. What must be the value of s for the equation to have equal roots?Class 10Quadratic EquationsNature of RootsLevel 37Expert MathematicsWhich quadratic equation will have two distinct real roots?Class 10Quadratic EquationsNature of RootsLevel 37Expert MathematicsWhich of the following equations has real, irrational, and distinct roots?Class 10Quadratic EquationsNature of RootsLevel 37Expert MathematicsWhich of the following quadratic equations has equal roots?Class 10Quadratic EquationsNature of RootsLevel 37Expert MathematicsWhat is the correct discriminant \(D\) of the quadratic equation \(x^2-2(k+1)x+k^2=0\)?Class 10Quadratic EquationsNature of RootsLevel 37Expert MathematicsAssertion: The graph of x² + 2x + 5 = 0 does not cut the x-axis. Reason: Its discriminant D = −16. Choose the correct option.Class 10Quadratic EquationsNature of RootsLevel 37Medium MathematicsAssertion: For the equation \(x^2-2(a+b)x+(a-b)^2=0\), if \(ab>0\), its roots are real and distinct. Reason: The discriminant of this equation is \(D=16ab\). Choose the correct option.Class 10Quadratic EquationsNature of RootsLevel 37Expert MathematicsFor real numbers \(p\) and \(q\), if \(q\ne0\), what is the nature of the roots of the equation \(x^2-2px+(p^2+q^2)=0\)?Class 10Quadratic EquationsNature of RootsLevel 37Expert MathematicsLet \(p\) 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 37Expert MathematicsFor 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 37Expert MathematicsFor the quadratic equation \(3x^2-2(2k+1)x+(k+1)^2=0\) to have equal roots, what are the values of \(k\)?Class 10Quadratic EquationsNature of RootsLevel 37Expert MathematicsIf the equation \(x^2+2(m-2)x+(m^2-3m+4)=0\) has no real roots, what is the correct condition on \(m\)?Class 10Quadratic EquationsNature of RootsLevel 37Expert MathematicsIf \\(x^2+2(m-2)x+(m^2-3m+4)=0\\) has equal roots, what is the value of \\(m\\)?Class 10Quadratic EquationsNature of RootsLevel 37Expert MathematicsThe equation (x^2-2(2t-1)x+(t^2+2)=0) has no real roots. Choose the correct interval for (t).Class 10Quadratic EquationsNature of RootsLevel 37Expert