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Subjects

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 the roots of a quadratic equation are \(b\) and \(-b\), what is the value of the ratio \(\frac{c}{a}\) of its constant term \(c\) to its leading coefficient \(a\)?If 8\alpha+\beta=-59 and 8\alpha\beta=-149, which monic quadratic equation has 8\alpha9 and 8\beta9 as its roots?What is the sum of the squares of the roots of the equation \(x^2-7x+10=0\)?If (x=3) is a root of (ax^2-8x+6=0), what is the value of (a)?For the quadratic equation \(x^2-18x+81=0\), what are the sum and product of its roots, respectively?If (\alpha) and (\beta) are roots of (2x^2-7x+3=0), what is the value of (\alpha+\beta-\alpha\beta)?If \(q(t)=0\) for the quadratic equation \(q(x)=0\), what is \(t\) called?Is \(x=5\) a root of the equation \(x^2-10x+25=0\)?Is \(x=-3\) a root of the equation \(2x^2+7x+3=0\)?What are the roots of the quadratic equation \(x^2-14x+45=0\)?What are the roots of the equation \(4x^2-17x+4=0\)?What are the roots of the equation \(5x^2+16x+3=0\)?Which quadratic equation has 3 and −8 as its roots?If (4) is a root of the equation (x^2+kx-32=0) , what is the value of (k) ?What is the sum of roots of 6x² − 13x + 5 = 0?What is the product of the roots of the equation \(7x^2+4x-9=0\)?What is the discriminant (D) of the quadratic equation \(4x^2-20x+25=0\)?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?Which statement is correct about the real roots of the equation \(x^2-6x+20=0\)?Which of the following quadratic equations has two distinct real roots?