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 x² − 7x + 11 = 0?If the quadratic equation \(x^2+kx+25=0\) has equal roots, what are the possible values of \(k\)?Which condition on \(k\) is necessary for the equation \(x^2-12x+k=0\) to have two real and distinct roots?What condition on \(k\) is necessary for the equation \(x^2+4x+k=0\) to have no real roots?If the equation \(2x^2-3x+p=0\) has real roots, which condition on \(p\) is correct?If the quadratic equation \(3x^2+mx+12=0\) has equal roots, what are the possible values of \(m\)?If the quadratic equation \(kx^2+8x+4=0\) has equal roots and \(k\neq0\), what is the value of \(k\)?Choose the correct condition on (k) for real roots of (4x^2+4kx+9=0).For the equation \(x^2-2(k+2)x+9=0\) to have equal roots, what are the possible values of \(k\)?For the quadratic equation \(x^2+(k-3)x+4=0\) to have no real roots, what is the interval of \(k\)?If \\(2x^2+(k+1)x+3=0\\) has two distinct real roots, which condition on \\(k\\) is correct?If the discriminant of a quadratic equation is \(D=18\), what is the nature of its roots?If an equation has (D=0), which statement is correct in terms of graph?If a parabola remains above the x-axis and does not intersect it, which statement is correct for the related quadratic equation?Which of the following quadratic equations has two real and distinct roots?A student writes the discriminant \(D=40\) for the equation \(x^2-4x+6=0\). What is the correct value of \(D\)?Assertion: The quadratic equation \(2x^2-8x+8=0\) has two equal roots. Reason: Its discriminant is \(D=0\). Choose the correct option.Assertion: The quadratic equation \(x^2+3x+7=0\) has no real roots.
Reason: If the discriminant \(D\) of a quadratic equation is less than zero, then it has no real roots.
Choose the correct option.What is the nature of the roots of the equation \(6x^2+7x-3=0\)?What is the correct conclusion about the nature of the roots of the quadratic equation \(8x^2-4x+3=0\)?