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 correct conclusion about the nature of the roots of \(7x^2+3x+2=0\)?What is the nature of the roots of the equation \(12x^2-12x+3=0\)?If \(a\ne0\), what is the condition for the quadratic equation \(ax^2+bx+c=0\) to have two equal real roots?What is the nature of the roots of the equation \(3x^2+x+4=0\)?What is the nature of the roots of the equation \\(10x^2-19x+6=0\\)?What is the nature of the roots of the equation \(2x^2-7x+1=0\)?If (D_1=64), (D_2=15), (D_3=0), and (D_4=-9), which one gives irrational distinct roots?For a quadratic equation with rational coefficients, if the discriminant is \(\Delta=144\), which statement correctly describes the nature of its roots?For which values of \(k\) will the quadratic equation \(x^2-2(k-5)x+36=0\) have equal roots?Which condition is correct for real roots in (2x^2+(2k+1)x+5=0)?For the quadratic equation \\(4x^2-9x+q=0\\) to have two real and equal roots, what should be the value of \\(q\\)?If the quadratic equation \(px^2-18x+9=0\) has equal roots and \(p\neq 0\), what is the value of \(p\)?Which condition is correct for real roots of (x^2+2(k+1)x+k+5=0)?An area-based problem leads to the equation \(r^2-10r+30=0\). What is the correct conclusion about the real values of \(r\)?A number-related problem leads to the equation \(n^2-21n+110=0\). What is the nature of the roots of this equation?Choose the correct statement about the nature of the roots of \(x^2+12x+37=0\).What is the nature of the roots of the equation \(5x^2-14x+11=0\)?What is the nature of the roots of the equation \(x^2-19x+90=0\)?What will be the nature of roots of (4x^2-5x-2=0)?Which condition on \(k\) ensures that the equation \(x^2-2(k-2)x+k^2=0\) has no real roots?