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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।

MathematicsWhat are the real roots of the equation \(2x^2-8=0\)?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Easy MathematicsFor the quadratic equation \(ax^2+bx+c=0\), under which condition will the roots be real?Class 10Quadratic EquationsRoots of a Quadratic EquationLevel 31Easy MathematicsWhat is the condition on p for the equation \(x^2+2px+49=0\) to have real roots?Class 10Quadratic EquationsIntroduction to Quadratic EquationsLevel 30Expert MathematicsWhich statement correctly describes the nature of the roots of \(x^2-10x+29=0\)?Class 10Quadratic EquationsIntroduction to Quadratic EquationsLevel 29Expert MathematicsWhat condition on \(p\) is necessary and sufficient for the equation \(x^2+2px+36=0\) to have real roots?Class 10Quadratic EquationsIntroduction to Quadratic EquationsLevel 29Expert MathematicsIf the roots of the equation \(x^2-2(k+1)x+k^2=0\) are real and distinct, what is the correct condition on \(k\)?Class 10Quadratic EquationsIntroduction to Quadratic EquationsLevel 28Expert MathematicsWhich statement correctly describes the nature of the roots of \(x^2-8x+17=0\)?Class 10Quadratic EquationsIntroduction to Quadratic EquationsLevel 28Expert MathematicsIf \(p\) is a real number, what is the condition for the equation \(x^2+2px+25=0\) to have real roots?Class 10Quadratic EquationsIntroduction to Quadratic EquationsLevel 28Expert MathematicsWhich of the following statements is correct for the equation \\(x^2-6x+11=0\\)?Class 10Quadratic EquationsIntroduction to Quadratic EquationsLevel 30Hard MathematicsWhat condition on \(k\) is necessary for the equation \(x^2+2kx+16=0\) to have real roots?Class 10Quadratic EquationsIntroduction to Quadratic EquationsLevel 30Hard MathematicsWhat condition on \(k\) is necessary and sufficient for the equation \(x^2+2kx+9=0\) to have real roots?Class 10Quadratic EquationsIntroduction to Quadratic EquationsLevel 29Hard MathematicsWhat is the maximum number of real solutions possible for 2x² + 7x + 3 = 0?Class 10Quadratic EquationsIntroduction to Quadratic EquationsLevel 29Easy MathematicsIf \(p(x)=x^2-6\sqrt{2}x+17\), what is the difference between its zeroes?Class 10PolynomialsIrrational numbers and real numbersLevel 25Expert MathematicsIf \(p(x)=x^2+6x+10\), how does its graph relate to the x-axis?Class 10PolynomialsGeometrical meaning of the zeroes of a polynomial.Level 24Expert MathematicsA polynomial's graph crosses the \(x\)-axis at \\((-5,0)\\) and touches the \(x\)-axis at \\((2,0)\\). Based on this information, what is the number of real (distinct) zeros?Class 10PolynomialsGeometrical meaning of the zeroes of a polynomial.Level 24Expert MathematicsIf the graph of a polynomial touches the x-axis at the single point (m, 0) and does not meet the x-axis anywhere else, how many distinct real zeros does the polynomial have?Class 10PolynomialsGeometrical meaning of the zeroes of a polynomial.Level 24Medium MathematicsIf the graph of a polynomial crosses the x-axis at \(x=1\) and only touches the x-axis at \(x=6\), how many distinct real zeros does the polynomial have?Class 10PolynomialsGeometrical meaning of the zeroes of a polynomial.Level 24Medium MathematicsIf \(p(x)=x^2+9\), how many times will its graph cut the x-axis?Class 10PolynomialsGeometrical meaning of the zeroes of a polynomial.Level 22Medium