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 two roots of the equation \(x^2+kx+9=0\) are equal, which value of \(k\) is possible?If the two roots of the equation \(x^2-2kx+16=0\) are equal, what is the value of \(k^2\)?For the quadratic equation \(ax^2+bx+c=0\), where \(a\ne0\), under which condition are its roots non-real?If the two roots of the equation \(kx^2+4x+1=0\) are equal, what is the value of \(k\)?For the roots of the equation \(2x^2+kx+2=0\) to be equal, what must be the value of \(k^2\)?Which of the following quadratic equations has real and distinct roots?Which of the following quadratic equations has real and equal roots?Which of the following quadratic equations has no real roots?Choose the correct statement about the nature of the roots of the equation \(x^2-10x+25=0\).What is the nature of roots in the equation (2x^2-7x+3=0)?Which statement correctly describes the nature of the roots of the equation \(6x^2+x+1=0\)?What is the discriminant \(D\) of the equation \(7x^2-10x+3=0\)?What is the nature of roots of the equation (7x^2-10x+3=0)?What is the discriminant \(D\) of the quadratic equation \(8x^2+8x+2=0\)?If the discriminant (D) of a quadratic equation is 4, which statement about its roots is correct?If the discriminant of a quadratic equation is \(D=-1\), which statement about its roots is correct?For the quadratic equation \(ax^2+bx+c=0\) \,\((a\ne0)\), the discriminant is \(D=b^2-4ac=0\). Which statement about its roots is correct?What is the nature of the roots of the equation \(x^2-12x+36=0\)?Which statement is correct about the real roots of the equation \(x^2-6x+13=0\)?If the roots of the quadratic equation \(x^2+px+4=0\) are real and distinct, which condition must \(p\) satisfy?