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Subjects

Mathematics

Nature of Roots

मूलों की प्रकृति

In Class 10 Mathematics, Nature of Roots explains how to determine the type and number of solutions of a quadratic equation. Students use the discriminant, b² − 4ac, to identify whether an equation has two distinct real roots, two equal real roots, or no real roots. The topic connects algebraic calculations with the graph of a quadratic function and helps learners interpret equations, compare cases, and solve related problems from the chapter Quadratic Equations.

Practice questions

If the discriminant \\(b^2-4ac=9\\) of a quadratic equation is 9, what will be the nature of its roots?If the discriminant of a quadratic equation is \\(b^2-4ac=-7\\), what is the correct conclusion about the nature of its roots?If (b^2-4ac=0), how many different real roots will a quadratic equation have?What is the discriminant \\(D\\) of the equation \\(4x^2+4x+1=0\\)?What is the nature of the roots of the equation \(4x^2+4x+1=0\)?What is the discriminant \(D\) of the quadratic equation \(x^2-2x-3=0\)?What is the nature of the roots of x²−2x−3=0?Find the value of the discriminant \(D\) for the quadratic equation \(5x^2+2x+1=0\).How many real roots does the equation (5x^2+2x+1=0) have?Which is the nature of roots in the equation (9x^2-6x+1=0)?What is the discriminant \(D\) of the equation \(2x^2+5x+2=0\)?State the nature of roots of the equation (2x^2+5x+2=0).What is the value of the discriminant \(D\) of the quadratic equation \(3x^2+2x+1=0\)?What is the nature of the roots of the quadratic equation \(3x^2+2x+1=0\)?Which of the following statements is correct for the equation \(x^2+6x+9=0\)?For the quadratic equation \\(x^2+7x+10=0\\), what is the value of the discriminant \\(D=b^2-4ac\\)?What will be the nature of the equation (x^2+7x+10=0)?What is the value of the discriminant \(D\) for the equation \(x^2+4x+8=0\)?Which conclusion about the nature of the roots of the equation \(x^2+4x+8=0\) is correct?If the two roots of the equation \(x^2+kx+9=0\) are equal, what is the correct condition for \(k\)?