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 D > 0 for a quadratic equation, what will be the nature of its roots?What is the discriminant D of 4x² + 4x + 1 = 0?What is the nature of the roots of x² + 6x + 9 = 0?If the roots of x² − 6x + k = 0 are equal, what is k?If the discriminant D = 49, what is the nature of the roots of the quadratic equation?If (D=64), what will be the nature of roots of the quadratic equation?Which equation has discriminant −15?If one root of x² + ax + 12 = 0 is 3, what are the other root and a?Which equation has discriminant −11?What is the nature of the roots of 4x² − 12x + 9 = 0?If D = 64 for a quadratic equation, what will be the nature of its real roots?What is the nature of the roots of 9x² − 24x + 16 = 0?What is the nature of the roots of 25x² − 30x + 9 = 0?For the general quadratic equation ax^2+bx+c=0, which relation is correct when the roots are equal?If the roots of (5x^2-4x+λ=0) are not real, what is the correct condition on (λ)?If D > 0, what type of roots does a quadratic equation have?If a quadratic equation has discriminant D = −4, which conclusion is correct?What is the correct statement about the real roots of x² + 25 = 0?If a quadratic equation has discriminant D = −9, which conclusion is correct?What is the correct statement about the real roots of x² + 36 = 0?