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 will λ be for real and equal roots of (λ+1)x² − 2(λ−2)x + (λ+1) = 0?If (2x^2-2(\mu+3)x+\mu^2+6\mu+5=0) has real and distinct roots, what is the condition on (\mu)?If a is a real number and \(x^2-2(a+4)x+a^2+8a+20=0\), how many real roots does the equation have?If \(a\) is a real parameter and \(x^2-2(a+4)x+a^2+8a+15=0\), what will be the nature of its roots?If \(a\) is a real number and \(x^2-2(a+4)x+(a^2+8a+16)=0\), what is the nature of its roots?What is the nature of the roots of \(2x^2-11x+15=0\)?Choose the correct conclusion about the nature of the roots of \(x^2+10x+29=0\).For the quadratic equation \(x^2-2kx+9=0\) to have real roots, which of the following conditions on \(k\) is required?What is the nature of roots of (x^2-2(a-5)x+a^2-10a+21=0)?What condition on \(k\) is necessary for the quadratic equation \(x^2+2(k+1)x+k^2+6k+9=0\) to have no real roots?What is the correct statement about the roots of ((p+4)x^2-2(p+1)x+(p-2)=0), if (p\neq-4)?If D>0 and D is not a perfect square, what is the nature of the roots of the quadratic equation?What is the nature of the roots of \(x^2-x-1=0\)?Choose the correct conclusion about the nature of the roots of the equation \(2x^2-x+2=0\).What is the value of the equal root of the equation \(9x^2-6x+1=0\)?What is the nature of the roots of the equation \(4x^2+7x-2=0\)?What is the nature of the roots of the equation \(x^2+11x+31=0\)?What is the nature of the roots of the equation \(3x^2-2x-2=0\)?Choose the correct statement about the nature and value of the roots of \\(16x^2+24x+9=0\\).Which statement correctly describes the nature of the roots of the quadratic equation \(5x^2+x+1=0\)?