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 \\(x=0\\) is a root of the equation \\(ax^2+bx+c=0\\), where \\(a\\ne0\\), which statement about \\(c\\) is correct?MediumLevel 31If \(x=1\) and \(x=4\) are the roots of a monic quadratic equation, what is the coefficient of \(x\)?MediumLevel 31What are the roots of the equation \(2x^2+x-6=0\)?MediumLevel 31The roots of the equation \(x^2+mx+12=0\) are \(-3\) and \(-4\). What is the value of \(m\)?MediumLevel 31If the roots of a quadratic equation are 4 and 1/4, which statement is correct about them?EasyLevel 31What is the positive root of the equation \(x^2-3x-18=0\)?MediumLevel 31If the discriminant \(D=0\) for a quadratic equation and the sum of its roots is 10, what is the value of each root?MediumLevel 31What is the absolute difference between the two roots of the equation \(x^2-4x-5=0\)?MediumLevel 31If \(\alpha\) and \(\beta\) are the roots of the equation \(2x^2-6x+1=0\), what is the value of \(\alpha+\beta\)?MediumLevel 31What is the nature of the roots of the quadratic equation \(x^2-6x+9=0\)?MediumLevel 31For the equation \(x^2+2x+k=0\) to have real roots, which condition on \(k\) is necessary?MediumLevel 31What will be the signs of both roots of (x^2+7x+10=0)?MediumLevel 31If both roots of the equation \(x^2+ax+9=0\) are \(3\), what is the value of \(a\)?MediumLevel 31What are the roots of the equation \(6x^2-7x+2=0\)?MediumLevel 31If the roots of a quadratic equation are (a) and (-a), what is the value of the ratio (\frac{c}{a_1}) of the constant term to the leading coefficient?MediumLevel 31If (alpha+beta=-3) and (alphabeta=-10), which monic quadratic equation has (alpha) and (beta) as its roots?MediumLevel 31What is the sum of the squares of the roots of \(x^2-6x+5=0\)?MediumLevel 31If (x=2) is a root of (ax^2-5x+2=0), what is the value of (a)?MediumLevel 31For the quadratic equation \(x^2-14x+49=0\), what are the sum and product of its roots, respectively?MediumLevel 31If the discriminant of a quadratic equation is \(D=b^2-4ac\) and \(D<0\), how many real roots does the equation have?MediumLevel 31