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
A student says that the equation \(x^2-6x+9=0\) has two distinct real roots because its discriminant is not less than zero. What is the error in the student's statement?MediumLevel 33Which statement is correct about the real roots of the equation \(x^2-6x+20=0\)?MediumLevel 33Which of the following quadratic equations has two distinct real roots?MediumLevel 33If the sum of roots is 11 and their product is 28, which monic quadratic equation is formed?MediumLevel 33One root of the equation \(x^2-17x+70=0\) is 7. What is the other root?MediumLevel 33If (4\alpha) and (4\beta) are new roots and (\alpha+\beta=3), what is the sum of the new roots?MediumLevel 33If the roots are (\alpha) and (\beta) with (\alpha+\beta=8) and (\alpha\beta=15), what is (\alpha^2+\beta^2)?MediumLevel 33If the roots of a quadratic equation are (4) and (-9), what is the value of (\frac{1}{\alpha}+\frac{1}{\beta})?MediumLevel 33For (5x^2-18x+9=0), what are the sum and product of roots respectively?MediumLevel 33If x + 6 and x − 2 are factors of a quadratic equation, what are its roots?MediumLevel 33If both roots of the equation \(x^2+px+36=0\) are \(-6\), what is the value of \(p\)?MediumLevel 33If (x=\frac{5}{2}) is a root of (2x^2-9x+c=0), what is the value of (c)?MediumLevel 33If a quadratic equation has \(a=1\), \(b=-20\), and \(c=100\), what are its roots?MediumLevel 33What condition must the discriminant of a quadratic equation satisfy for it to have two real and equal roots?MediumLevel 33What are the roots of (x^2+2x-35=0)?MediumLevel 33If (alpha) and (beta) are the roots of (x^2-9x+20=0), what is the value of (alpha+beta+alphabeta)?MediumLevel 33If the sum of the roots of a quadratic equation is 0 and their product is −36, which is its monic equation?MediumLevel 33What is the repeated root of the equation \(25x^2-10x+1=0\)?MediumLevel 33If \(x=0\) is a root of the equation \(2x^2+mx+n=0\), what is the value of \(n\)?MediumLevel 33If (x=3) and (x=8) are roots of a monic quadratic equation, what will be the coefficient of (x)?MediumLevel 33