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 equal root of (x^2-8x+16=0)?What is the nature of roots of (x^2-3x+1=0)?Choose the correct statement about the nature of the roots of \(2x^2-5x+2=0\).What is the nature of the roots of the equation \(3x^2-12=0\)?For the equation \(5x^2+2x+1=0\), what is the sign of the discriminant \(D\) and the nature of its roots?If the graph of a quadratic equation touches the x-axis at exactly one point, what is the nature of its roots?If the graph of a parabola intersects the x-axis at two distinct points, what will be the nature of the roots of the corresponding quadratic equation?If the parabola representing a quadratic equation neither intersects nor touches the x-axis, what can be concluded about its real roots?If (2x^2-8x+c=0) has equal roots, what is the value of (c)?If the quadratic equation \(4x^2+mx+1=0\) has equal roots, what are the possible values of \(m\)?If the quadratic equation \(px^2+4x+1=0\) has equal roots and \(p\neq 0\), what is the value of \(p\)?Which condition on \(k\) is necessary for the quadratic equation \(3x^2+2kx+k=0\) to have real roots?If the quadratic equation \(kx^2-6x+1=0\) has equal roots, what is the value of \(k\)?For the equation \(x^2-(k+1)x+4=0\), in which interval must \(k\) lie for the equation to have no real roots?Choose the correct condition on \(k\) for the equation \(x^2+2(k+1)x+k^2=0\) to have two distinct real roots.A student says that the equation \(x^2-2x+5=0\) has two real roots because \(b^2\) is positive. What is the correct evaluation of this statement?If the discriminant of a quadratic equation is D = 49, what is the nature of its roots?If the coefficients of a quadratic equation are rational and its discriminant is D = 12, what is the nature of its roots?Which condition identifies that the quadratic equation \(ax^2+bx+c=0\), where \(a\ne0\), has two equal real roots?Assertion: The equation \(x^2-10x+25=0\) has equal roots. Reason: Its discriminant is \(D=0\). Choose the correct option.