Mathematics
Roots of a Quadratic Equation
द्विघात समीकरण के मूल
Roots of a Quadratic Equation, taught in Class 10 Mathematics under the chapter Quadratic Equations, introduces the values of the variable that make a quadratic expression equal to zero. Students learn to identify roots, verify them by substitution, and connect the sum and product of the roots with the coefficients. The topic also helps them form a quadratic equation when its roots are known and use these relationships to solve and check mathematical problems.
Practice questions
What is the product of the roots of \\(3x^2+8x-11=0\\)?MediumLevel 31What is the discriminant \(D\) of the quadratic equation \(2x^2-4x+2=0\)?MediumLevel 31If (D=49) for a quadratic equation, what will be the nature of its real roots?MediumLevel 31Which statement is correct about the roots of the equation \(x^2-2x+10=0\)?MediumLevel 31For the equation \(x^2-6x+k=0\) to have two equal real roots, what should be the value of \(k\)?MediumLevel 31If the sum of the roots of a quadratic equation is 7 and their product is 10, which monic quadratic equation is formed?MediumLevel 31If one root of the equation \(x^2-13x+40=0\) is \(5\), what is the other root?MediumLevel 31If (2\alpha) and (2\beta) are roots and (\alpha+\beta=5), what is the sum of the new roots?MediumLevel 31If the roots are (\alpha) and (\beta) with (\alpha+\beta=6) and (\alpha\beta=8), what is (\alpha^2+\beta^2)?MediumLevel 31If the roots of a quadratic equation are (3) and (-4), what is the value of (\frac{1}{\alpha}+\frac{1}{\beta})?MediumLevel 31For 2x² − 9x + 4 = 0, what are the sum and product of the roots respectively?MediumLevel 31If (x+2) and (x-5) are factors of a quadratic equation, what are its roots?MediumLevel 31If both roots of the equation x² + px + 16 = 0 are -4 and -4, what is the value of p?MediumLevel 31If (x=\frac{3}{2}) is a root of (2x^2-5x+c=0), what is the value of (c)?MediumLevel 31If the standard quadratic equation \(ax^2+bx+c=0\) has \(a=1\), \(b=-10\), and \(c=25\), what are its roots?MediumLevel 31If the product of roots of a quadratic equation is (0), which statement is correct?MediumLevel 31What are the roots of the quadratic equation \(x^2-2x-15=0\)?MediumLevel 31If \(\alpha\) and \(\beta\) are the roots of the equation \(x^2-5x+6=0\), what is the value of \(\alpha+\beta+\alpha\beta\)?MediumLevel 31If the sum of the roots of a quadratic equation is 0 and their product is −16, which monic equation is formed?MediumLevel 31What is the repeated root of the equation \(9x^2-6x+1=0\)?MediumLevel 31