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 \(4x^2+4x+5=0\)?Which pair correctly gives the discriminant \(\Delta\) and the nature of the roots of \(x^2+5x+6=0\)?What is the sign of the discriminant \(D\) for the equation \(3x^2-2x+4=0\)?What is the sign of the discriminant (D) of the equation \(2x^2+4x+2=0\)?What is the nature of the roots of the equation \(x^2-11x+30=0\)?Choose the correct answer for (x^2+14x+49=0).What is the nature of the roots of the equation \(x^2-4x+8=0\)?What is the value of s for equal real roots of x² − 3x + s = 0?For the quadratic equation \(5x^2-4x+t=0\) to have real and equal roots, what is the value of \(t\)?Read the statement: The equation \(x^2+1=0\) has no real roots because its discriminant is \(D<0\). How is this statement?What is the nature of the roots of the equation \\(3x^2+10x+3=0\\)?Which quantity is used to determine the nature of the roots of the quadratic equation \(ax^2+bx+c=0\), where \(a\ne0\)?If the discriminant \(D\) of the quadratic equation \(ax^2+bx+c=0\) is greater than zero, what will be the nature of its roots?For a quadratic equation with real coefficients, if the discriminant \(D<0\), what is the nature of its roots?What is the value of the discriminant \(D\) for the equation \(x^2-5x+6=0\)?What is the nature of the roots of the quadratic equation \(x^2-4x+4=0\)?What is the discriminant \(D\) of the quadratic equation \(2x^2-3x+1=0\)?What will be the nature of the roots of 2x²−3x+1=0?What is the nature of roots for the equation (3x^2+6x+3=0)?What is the sign of the discriminant \(D\) for the equation \(x^2+x+1=0\)?