Mathematics
Introduction to Quadratic Equations
द्विघात समीकरणों का परिचय
Introduction to Quadratic Equations, part of the Class 10 Mathematics chapter Quadratic Equations, helps students recognise equations of degree two and write them in the standard form ax² + bx + c = 0, where a ≠ 0. Students learn the meaning of coefficients, variables, and constants, identify quadratic equations from examples, and understand how their roots or solutions relate to the equation. The topic builds a foundation for solving quadratic equations by methods such as factorisation and applying the quadratic formula.
Practice questions
What is the maximum number of real solutions possible for (x^2+3x+2=0)?EasyLevel 28For the equation \(4x^2+4x+1=0\), if the quadratic is written as \(ax^2+bx+c=0\), what is the value of \(a+b+c\)?EasyLevel 28For the quadratic equation \(2x^2-3x-5=0\), what is the value of \(a-b+c\)? (Here \(a,b,c\) are the coefficients in \(ax^2+bx+c=0\).)EasyLevel 28What is the degree of the equation \(5x^2+2x-1=0\)?EasyLevel 28Which of the following is the factorised form of \(x^2-2x-15=0\)?EasyLevel 28A rectangle has length \(x+3\) and width \(x\). If its area is \(10\), which equation represents this situation?EasyLevel 28The product of two consecutive positive integers is 30. If the smaller integer is \(x\), which of the following equations represents this situation?EasyLevel 28Which option shows the common mistake when converting the equation \(x^2 = 5x - 6\) to standard form?EasyLevel 28Which equation has (x=0) as a solution?EasyLevel 28If x² + kx + 12 = 0 is a quadratic equation, then k is the coefficient of which term?EasyLevel 29In the equation \(7x^2+2x-5=0\), what is the value of \(a\)?EasyLevel 29What is the value of b in the quadratic equation \(5x^2-9x+4=0\)?EasyLevel 29In the equation \(8x^2+3x+12=0\), what is the value of \(c\)?EasyLevel 29In the quadratic equation \(11x^2-6x=0\), what is the value of the constant term \(c\)?EasyLevel 29In the equation \(13x^2-20=0\), what is the value of \(b\) in the standard quadratic form \(ax^2+bx+c=0\)?EasyLevel 29Under which condition will the equation \(px^2+qx+r=0\) be called a quadratic equation?EasyLevel 29What is the standard form of \(4x^2+7x=9\)?EasyLevel 29What is the standard form of the equation \(2x^2=5x+3\)?EasyLevel 29If \(x=3\), what is the left-hand side of \(x^2-4x+3=0\)?EasyLevel 29Which of the following is a solution of the equation \(x^2-25=0\)?EasyLevel 29