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 are the roots of \\(4x^2+3x-10=0\\)?MediumLevel 33If the roots of the quadratic equation \(x^2+mx+30=0\) are \(-5\) and \(-6\), what is the value of \(m\)?MediumLevel 33If the roots of a quadratic equation are 6 and 1/6, which statement is correct about them?MediumLevel 33What is the positive root of the equation \(x^2-7x-30=0\)?MediumLevel 33If the discriminant of a quadratic equation is \(D=0\) and the sum of its roots is \(14\), what is the value of each root?MediumLevel 33What is the positive difference between the two roots of the equation \(x^2-8x-9=0\)?MediumLevel 33Which of the following quadratic equations has two equal real roots?MediumLevel 33If α and β are roots of 6x² + 5x − 4 = 0, what is αβ?MediumLevel 33What is the necessary and sufficient condition on \(k\) for the equation \(x^2+6x+k=0\) to have real roots?MediumLevel 33What will be the signs of both roots of (x^2+13x+42=0)?MediumLevel 33If the roots of the equation \(x^2+ax+25=0\) are \(5\) and \(5\), what is the value of \(a\)?MediumLevel 33What are the roots of the equation \(10x^2-17x+3=0\)?MediumLevel 33If the roots of a quadratic equation \(ax^2+bx+d=0\) are \(c\) and \(-c\), what is the value of the ratio \(\frac{d}{a}\) of the constant term to the leading coefficient?MediumLevel 33If (alpha+beta=-7) and (alphabeta=-18), which monic quadratic equation has alpha and beta as its roots?MediumLevel 33What is the sum of the squares of the roots of the equation \(x^2-9x+14=0\)?MediumLevel 33If x = 4 is a root of ax² − 10x + 8 = 0, what is the value of a?MediumLevel 33For the quadratic equation \(x^2-22x+121=0\), what are the sum and product of its roots, respectively?MediumLevel 33If (\alpha) and (\beta) are roots of (4x^2-5x-6=0), what is the value of (\alpha+\beta-2\alpha\beta)?MediumLevel 33If (\alpha) and (\beta) are roots of (x^2-7x+12=0), what is the value of (\frac{\alpha}{\beta}+\frac{\beta}{\alpha})?HardLevel 31If (\alpha) and (\beta) are roots of (x^2-5x+6=0), what is the value of ((\alpha-\beta)^2)?HardLevel 31