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 be the nature of roots of (2x^2+5x-12=0)?If (x^2-3x+h=0) has equal roots, what is the value of (h)?What is the nature of roots of (8x^2-8x+3=0)?If the roots of the quadratic equation \(3x^2-2kx+27=0\) are equal, what are the possible values of \(k\)?What is the nature of roots of \(x^2+\frac{1}{2}x+\frac{1}{16}=0\)?How are the roots of \(4x^2+\frac{4}{3}x+\frac{1}{9}=0\)?If (x^2+px+q=0) has two equal real roots, which relation is correct?If (b^2=4ac) in a quadratic equation, what will be the nature of its roots?If (x^2-2(k+3)x+(k^2+6k+5)=0), what will be the nature of its roots?If (kx^2-6x+9=0) has real roots, what is the correct condition for (k)?Which conclusion is correct for equal real roots of ((m-2)x^2+2mx+(m+2)=0)?If (a\neq0) and (b^2-4ac) is a positive perfect square in (ax^2+bx+c=0), what is the most accurate nature of the roots?What is the nature of the roots of the equation \(4x^2-4\sqrt{3}x+3=0\)?Choose the correct conclusion about the nature of the roots of \(x^2-2\sqrt{5}x+6=0\).If \(k\) is a real number and the roots of the equation \(x^2-2(k+1)x+(k^2+4)=0\) are real, what is the correct condition on \(k\)?What condition on \(m\) is necessary for the equation \(x^2-(m+3)x+3m=0\) to have two real and distinct roots?For the equation \((p+1)x^2-2(p+2)x+(p+4)=0\), where \(p\ne -1\), what condition on \(p\) ensures that the roots are real?For what value of \(k\) will the quadratic equation \(2x^2-(k+4)x+2k=0\) have equal roots?For which value of \(k\) will the two roots of the quadratic equation \(2x^2-(k+4)x+2k=0\) be equal?If (x^2+2(k-1)x+(k+5)=0) has no real roots, in which interval will (k) lie?