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
What is the nature of the roots of the quadratic equation \(2x^2+5x+2=0\)?What is the nature of the roots of the quadratic equation \(9x^2-6x+1=0\)?What is the nature of the roots of the equation \(x^2+x+3=0\)?What is the discriminant of the equation \(6x^2-5x+1=0\)?What is the correct conclusion about the nature of the roots of the equation \(7x^2+2x+3=0\)?For (x^2-2x+n=0) to have two real and distinct roots, which condition is correct?For (x^2+4x+p=0) to have no real roots, which condition is correct?For the quadratic equation \\(x^2 - 10x + r = 0\\) to have two equal real roots, what is the value of \\(r\\)?Which value of k can give equal real roots for the equation 3x² + kx + 12 = 0?For the equation \(2x^2+3x+\lambda=0\) to have real and distinct roots, which condition on \(\lambda\) is correct?Which statement correctly describes the nature of the roots of \(x^2+12x+36=0\)?What is the nature of the roots of the equation \(x^2-9=0\)?Choose the correct statement about the nature of the roots of the equation \(x^2+9=0\).What is the nature of the roots of the equation \(4x^2-1=0\)?What is the nature of the roots of the equation \\(2x^2+8=0\\)?Which quadratic equation has a pair of non-real (imaginary) roots?If the standard quadratic equation \(ax^2+bx+c=0\) has two distinct real roots, what will be the value condition for its discriminant \(D=b^2-4ac\)?If the quadratic equation \(ax^2+bx+c=0\) has no real roots, what is the correct condition for the discriminant \(D=b^2-4ac\)?Which of the following statements is correct for the equation \\(x^2-6x+9=0\\)?What is the nature of the roots of the equation \(2x^2-7x+3=0\)?