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
If α is a root of p(x) = 0, which statement is correct?Which quadratic equation has roots x = 1 and x = 4?If the sum of the roots of 2x² + mx + 8 = 0 is −3, what is m?Which pair is the correct set of roots of x² − 2x − 15 = 0?Which quadratic equation has roots x = 2 and x = 7?If x = −5 and x = 2 are roots, what is the sum of the roots?If x = −3 is a root of 2x² + rx − 9 = 0, what is r?Which equation has roots x = 3 and x = 8?If x = −6 and x = 1 are roots, what is the sum of the roots?What is the product of the roots of 6x² + 5x − 14 = 0?If x = 1 is not a root of kx² − 5x + 2 = 0, what condition must k satisfy?If α and β are roots of x² + 3x − 18 = 0, what is αβ − α − β?If one root of x² + ax + 18 = 0 is 2, what are the other root and a?If the roots of a monic quadratic equation are r and 2r, and their sum is 9, what is the constant term?If one root of x² + ax + 24 = 0 is 4, what are the other root and a?If the roots of a monic quadratic equation are r and 3r, and their sum is 16, what is the constant term?If α and β are roots of x² − 6x − 27 = 0, what is αβ + 3α + 3β?If one root of x² + ax + 40 = 0 is 5, what are the other root and a?If α and β are roots of x² − 7x − 30 = 0, what is αβ + 4α + 4β?What is called a root of a quadratic equation?