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
How will the roots of 3x² − 6x + 1 = 0 be?What is the value of the discriminant \(D\) of the quadratic equation \(x^2+8x+16=0\)?What is the nature of the roots of the quadratic equation \(x^2+8x+16=0\)?What is the discriminant \(D\) of the quadratic equation \(2x^2+7x+3=0\)?What is the nature of the roots of the equation 2x² + 7x + 3 = 0?For the quadratic equation \\(7x^2+2x+3=0\\), the discriminant is \\(D=b^2-4ac\\). What is the value of \\(D\\)?Which statement correctly describes the nature of the roots of \(7x^2+2x+3=0\)?If the two roots of the quadratic equation \(x^2-2rx+9=0\) are equal, what is the value of \(r^2\)?If the roots of the quadratic equation \(4x^2+sx+9=0\) are real and equal, what is the value of \(s^2\)?What is the nature of roots of the equation (x^2-5x+3=0)?If the equation \(x^2+tx+12=0\) has no real roots, what is the correct condition on \(t\)?If the discriminant of the quadratic equation \\(ax^2+bx+c=0\\) is \\(D=b^2-4ac\\), what is the nature of its roots when \\(D>0\\)?State the nature of roots of (x^2-5x+6=0).What is the nature of the roots of the equation \(x^2+4x+4=0\)?Choose the correct statement about the nature of the roots of the equation \(2x^2+x+3=0\).How will the roots of x² − 2x − 3 = 0 be?If the two roots of the equation \(x^2-4x+k=0\) are equal, what is the value of \(k\)?If the quadratic equation \(x^2+kx+9=0\) has equal roots, which values of \(k\) are possible?What condition on \(k\) is necessary for the equation \(x^2-6x+k=0\) to have two real and distinct roots?Which condition on \(k\) ensures that the equation \(x^2+2x+k=0\) has no real roots?