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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।

MathematicsWhich quadratic equation has real and distinct roots?Class 10Quadratic EquationsNature of RootsLevel 37Expert MathematicsIf \(a\) 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 37Expert MathematicsFor real numbers a and b, if the equation \(x^2-2(a+b)x+(a-b)^2=0\) has real and distinct roots, which condition on a and b is correct?Class 10Quadratic EquationsNature of RootsLevel 37Expert MathematicsIf \(k\neq 0\) and \(kx^2-2(k+1)x+(k+3)=0\) is a quadratic equation, what must be the value of \(k\) for it to have equal roots?Class 10Quadratic EquationsNature of RootsLevel 37Expert MathematicsIf \(k\) is a real number, what is the correct condition for the equation \(x^2+2(k-1)x+(k+5)=0\) to have no real roots?Class 10Quadratic EquationsNature of RootsLevel 37Expert MathematicsFor which value of \(k\) will the two roots of the quadratic equation \(2x^2-(k+4)x+2k=0\) be equal?Class 10Quadratic EquationsNature of RootsLevel 37Expert MathematicsFor what value of \(k\) will the quadratic equation \(2x^2-(k+4)x+2k=0\) have equal roots?Class 10Quadratic EquationsNature of RootsLevel 37Expert MathematicsFor 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 37Expert MathematicsWhat condition on \(m\) is necessary for the equation \(x^2-(m+3)x+3m=0\) to have two real and distinct roots?Class 10Quadratic EquationsNature of RootsLevel 37Expert MathematicsIf \(k\) 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 37Expert MathematicsChoose the correct conclusion about the nature of the roots of \(x^2-2\sqrt{5}x+6=0\).Class 10Quadratic EquationsNature of RootsLevel 37Expert MathematicsWhat is the nature of the roots of the equation \(4x^2-4\sqrt{3}x+3=0\)?Class 10Quadratic EquationsNature of RootsLevel 37Expert MathematicsIf (a\neq0) and (b^2-4ac) is a positive perfect square in (ax^2+bx+c=0), what is the most accurate nature of the roots?Class 10Quadratic EquationsNature of RootsLevel 37Expert MathematicsWhich conclusion is correct for equal real roots of ((m-2)x^2+2mx+(m+2)=0)?Class 10Quadratic EquationsNature of RootsLevel 39Hard MathematicsIf (kx^2-6x+9=0) has real roots, what is the correct condition for (k)?Class 10Quadratic EquationsNature of RootsLevel 39Hard MathematicsIf (x^2-2(k+3)x+(k^2+6k+5)=0), what will be the nature of its roots?Class 10Quadratic EquationsNature of RootsLevel 39Hard MathematicsIf (b^2=4ac) in a quadratic equation, what will be the nature of its roots?Class 10Quadratic EquationsNature of RootsLevel 39Hard MathematicsIf (x^2+px+q=0) has two equal real roots, which relation is correct?Class 10Quadratic EquationsNature of RootsLevel 39Hard MathematicsHow are the roots of \(4x^2+\frac{4}{3}x+\frac{1}{9}=0\)?Class 10Quadratic EquationsNature of RootsLevel 39Hard MathematicsWhat is the nature of roots of \(x^2+\frac{1}{2}x+\frac{1}{16}=0\)?Class 10Quadratic EquationsNature of RootsLevel 39Hard