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 x² − 12x + k = 0 has equal roots, what is the value of k?Which expression is used to determine the nature of the roots of the quadratic equation \(ax^2+bx+c=0\)?If the discriminant (D>0) of a quadratic equation is positive, what is the nature of its roots?For a quadratic equation, if the discriminant \(D=b^2-4ac=0\), what will be the nature of its roots?What is the nature of the roots of the equation \(x^2-5x+6=0\)?What is the nature of the roots of the equation \(x^2-4x+4=0\)?Which statement correctly describes the nature of the roots of \(x^2+2x+5=0\)?What is the value of the discriminant \\(\Delta\\) for the equation \\(2x^2-3x+1=0\\)?What is the nature of the roots of the equation \(3x^2+6x+3=0\)?What is the nature of the roots of the quadratic equation \(5x^2+x+1=0\)?For the quadratic equation \(x^2+6x+k=0\) to have equal real roots, what should be the value of \(k\)?For the equation \\(x^2-8x+m=0\\), what is the value of \\(m\\) if its roots are real and equal?Which of the following values of \(k\) can make the equation \(x^2+kx+16=0\) have equal real roots?Which equation will have two real and distinct roots?Which of the following quadratic equations will have two real and equal roots?Which of the following quadratic equations will have no real roots?What is the nature of the roots of the quadratic equation \(4x^2-12x+9=0\)?If the discriminant of a quadratic equation is \(D=25\), what will be the nature of its roots?If the discriminant of a quadratic equation is \(D=-7\), what will be the nature of its roots?If (D=0) and (a\neq0), how many distinct real roots will the quadratic equation have?