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
Choose the correct statement about the nature and value of the roots of \\(16x^2+24x+9=0\\).MediumLevel 39Which statement correctly describes the nature of the roots of the quadratic equation \(5x^2+x+1=0\)?MediumLevel 39What is the nature of the roots of the equation \\(6x^2-13x+6=0\\)?MediumLevel 39If (x^2-14x+k=0) has equal roots, what is the value of (k)?MediumLevel 39If the two roots of the equation \(x^2+kx+36=0\) are equal, what are the possible values of \(k\)?MediumLevel 39Which condition on \(k\) is required for the equation \(x^2-16x+k=0\) to have two real and distinct roots?MediumLevel 39What condition on \(k\) is necessary for the equation \(x^2+6x+k=0\) to have no real roots?MediumLevel 39If the roots of the quadratic equation \(3x^2-4x+p=0\) are real, which condition on \(p\) is correct?MediumLevel 39If the two roots of \(2x^2+mx+18=0\) are equal, what are the possible values of \(m\)?MediumLevel 39If the quadratic equation \(kx^2+10x+5=0\) has equal roots and \(k\ne0\), what is the value of \(k\)?MediumLevel 39Which condition on \\(k\\) is necessary for the equation \\(5x^2+2kx+2=0\\) to have real roots?MediumLevel 39For the equation \(x^2-2(k+4)x+25=0\) to have equal roots, what are the values of \(k\)?MediumLevel 39For which interval of \(k\) does the equation \(x^2+(k+2)x+9=0\) have no real roots?MediumLevel 39If the equation \\(3x^2+(k-2)x+4=0\\) has two distinct real roots, which condition on \\(k\\) is correct?MediumLevel 39If a quadratic equation with rational coefficients has discriminant \(\Delta=27\), what is the nature of its roots?MediumLevel 39If a quadratic equation has D=-12, which statement is correct regarding its graph?MediumLevel 39If the parabola of a quadratic equation with rational coefficients cuts the x-axis at two distinct points and its discriminant \(D\) is not a perfect square, what will be the nature of its roots?MediumLevel 39Which of the following equations has two real, rational and distinct roots?MediumLevel 39A student writes \(D=49\) for the quadratic equation \(2x^2-3x+5=0\). What is the correct value of the discriminant \(D\)?MediumLevel 39Assertion: The quadratic equation \(7x^2-14x+7=0\) has equal roots. Reason: Its discriminant is \(D=0\). Choose the correct option.MediumLevel 39