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 discriminant \(D\) of the equation \(5x^2-20x+20=0\)?What is the nature of the roots of the equation \(5x^2-20x+20=0\)?If a quadratic equation with rational coefficients has discriminant \(D=25\), what will be the nature of its roots?If the coefficients of a quadratic equation are integers and its discriminant (D) is 5, what is the correct conclusion?If the discriminant of a quadratic equation with real coefficients is \(D=-9\), which statement about its roots is correct?If the two roots of the quadratic equation \(x^2+kx+16=0\) are equal, what is the value of \(k^2\)?Which of the following quadratic equations has roots of opposite signs?If the roots of the equation \(x^2+px+6=0\) are real and distinct, which of the following conditions on \(p\) is correct?If the equation \(x^2+qx+10=0\) has no real roots, what is the correct condition on \(q\)?If the two roots of the quadratic equation \(mx^2+6x+3=0\) are equal, what is the value of \(m\)?If the two roots of the equation \(2x^2+nx+8=0\) are equal, what is the value of \(n^2\)?Which of the following quadratic equations has real, rational, and distinct roots?Which of the following quadratic equations has real, irrational, and distinct roots?Statement: When (D=0), roots are equal. What type of statement is this?Statement: If the discriminant \(D<0\), the equation has two real and distinct roots. What type of statement is this?Statement: If the discriminant \(D>0\) for a quadratic equation, then its roots are always equal. Choose the correct option.What is the nature of the roots of the equation \(4x^2-4x+3=0\)?What is the discriminant \(D\) of the quadratic equation \(6x^2-5x+1=0\)?What is the nature of the roots of the equation \(6x^2-5x+1=0\)?What is the discriminant \(D\) of the quadratic equation \(3x^2-6x+1=0\)?