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 \(\alpha\) and \(\beta\) are the roots of the equation \(x^2-2x-8=0\), what is the value of \(\left(\alpha+3\right)\left(\beta+3\right)\)?If the two roots of the equation \(x^2+kx+36=0\) are equal and negative, what is the value of \(k\)?If (\alpha) and (\beta) are roots of (x^2-12x+32=0), what is the value of (\frac{\alpha^2+\beta^2}{\alpha\beta})?If the roots of the quadratic equation \(2x^2+px+8=0\) are \(-1\) and \(-4\), what is the value of \(p\)?If a new equation is formed by taking reciprocals of the roots of (x^2-5x+6=0), which monic equation is obtained?If (\alpha) and (\beta) are roots of (x^2-8x+15=0), what is the value of (\frac{\alpha}{\beta}+\frac{\beta}{\alpha})?If (\alpha) and (\beta) are roots of (x^2-9x+20=0), what is the value of ((\alpha-\beta)^2)?What is the positive difference between the two roots of (x^2-2kx+(k^2-4)=0)?If 3 and 5 are the roots of the equation \(ax^2+bx+15=0\), what is the value of \(a\)?If the roots of (x^2-(m+3)x+18=0) are (3) and (6), what is the value of (m)?If the roots of the equation \(x^2+px+q=0\) are \(-3\) and \(-4\), what is the value of \(p+q\)?What is the sum of reciprocals of the roots of (3x^2-10x+3=0)?If \(\alpha\) and \(\beta\) are the roots of the equation \(x^2-10x+21=0\), what is the value of \(\alpha^3+\beta^3\)?If the two roots of the quadratic equation \(x^2-6x+k=0\) are real and equal, what is the value of \(k\)?If the equation \(kx^2-8x+16=0\) has equal roots and \(k\ne0\), what is the value of \(k\)?How many real roots does the equation \(x^2+4x+13=0\) have?If roots of x^2-(a+2)x+2a=0 are 2 and a, which reason is correct?If \(\alpha\) and \(\beta\) are the roots of the equation \(x^2-8x+12=0\), what is the value of \((\alpha+2)(\beta+2)\)?If (\alpha) and (\beta) are roots of (x^2-4x-21=0), what is the value of (\alpha^2\beta+\alpha\beta^2)?If (\alpha) and (\beta) are roots of (3x^2-8x+4=0), what is the value of (\frac{1}{\alpha^2}+\frac{1}{\beta^2})?