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
A rectangle's length is 4 units more than its breadth and its area is 45 square units. If the breadth is x, what is the equation?MediumLevel 28What are the roots of the equation \(x^2-8x=0\)?MediumLevel 28What are the roots of (9x^2-25=0)?MediumLevel 28Which factorised form represents the equation \(x^2+7x+12=0\)?MediumLevel 28In the equation \(2x^2+7x+3=0\), what is the value of \(ac\)?MediumLevel 28Which of the following quadratic equations of the form \(ax^2+bx+c=0\) has \(b=0\) and \(c<0\)?MediumLevel 28How will (\frac{x^2}{2}+3x-5=0) be written in standard form without fractions?MediumLevel 28What is the equivalent equation with integer coefficients for \(\frac{1}{3}x^2-\frac{2}{3}x+1=0\)?MediumLevel 28Which option is not a quadratic equation?MediumLevel 28What is the value of (b) in (x^2+2\sqrt{3}x+3=0)?MediumLevel 28If (x=2) and (x=-3) are roots of a quadratic equation, what is the sum of the roots?MediumLevel 28If the roots are (4) and (6), what is the product of the roots?MediumLevel 28Which quadratic equation has roots whose sum is 5 and product is 6?MediumLevel 28What is the sum of roots of (2x^2-5x+3=0)?MediumLevel 28What is the product of the roots of the equation \(3x^2+2x-8=0\)?MediumLevel 28If the product of the roots of \(kx^2-4x+2=0\) is 1, what is the value of \(k\)?MediumLevel 28In which equation is (x=1) not a root?MediumLevel 28If the roots of \(x^2+px+16=0\) are 4 and 4, what is the value of \(p\)?MediumLevel 28Which quadratic equation is obtained by simplifying ((x+2)^2-(x+2)-6=0)?MediumLevel 28What is the standard form of ((x-1)(x+6)=2x)?MediumLevel 28