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 equation \\(5x^2-30x+45=0\\)?What is the discriminant of \\(x^2+9x+14=0\\), and what is the nature of its roots?What is the nature of the roots of \\(2x^2+x+2=0\\)?What is the nature of the roots of the equation \(7x^2-9x+2=0\)?What is the nature of the roots of the equation \(x^2-3x-1=0\)?If (D_1=36), (D_2=11), (D_3=0), and (D_4=-5), which one gives irrational distinct roots?For a quadratic equation \(ax^2+bx+c=0\), where \(a,b,c\) are rational numbers and \(a\ne0\), if the discriminant \(D=b^2-4ac=100\), which statement correctly describes the roots?For which values of \\(k\\) will the equation \\(x^2-2(k-3)x+16=0\\) have equal roots?Which condition is correct for real roots in (3x^2+(2k-1)x+1=0)?For the quadratic equation \(2x^2-5x+q=0\) to have two real and equal roots, what should be the value of \(q\)?If the quadratic equation \(px^2-14x+7=0\) has equal roots and \(p\ne0\), what is the value of \(p\)?Which condition on \(k\) is necessary and sufficient for the equation \(x^2+2(k-1)x+k+2=0\) to have real roots?An area-based problem leads to the equation \(s^2-6s+10=0\). What is the correct conclusion about the real values of \(s\)?A number-related problem leads to the equation \(n^2-15n+56=0\). What is the nature of the roots of this quadratic equation?Choose the correct statement about the nature of the roots of \\(x^2+8x+18=0\\).What is the nature of the roots of the equation \(4x^2-12x+11=0\)?What is the nature of the roots of the quadratic equation \(x^2-13x+40=0\)?What will be the nature of roots of (3x^2-4x-1=0)?For the equation \\((r+2)x^2-2(r+5)x+(r+2)=0\\), what is the value of \(r\) for which the roots are real and equal?If m is a real number, when will the roots of \(x^2-2(m-4)x+m^2-16=0\) be real and distinct?