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 nature of roots of (x^2-10x+25=0)?MediumLevel 29What is the sign of the discriminant (D) of the equation \(3x^2+2x+7=0\)?MediumLevel 29If the roots are -4 and 3, what is the monic quadratic equation?MediumLevel 29The square of a number \(x\) is 24 more than 5 times the number. Which equation represents this?MediumLevel 29The sum of the squares of two consecutive integers is 85. If the smaller integer is \(x\), which equation represents this relationship?MediumLevel 29A rectangle's length is 6 units more than its breadth and its area is 72 square units. If the breadth is x, what is the equation?MediumLevel 29What are the roots of \(x^2+9x=0\)?MediumLevel 29What are the roots of (16x^2-81=0)?MediumLevel 29Which factored form represents \(x^2+9x+20=0\)?MediumLevel 29In the equation \(3x^2+10x+8=0\), what is the value of \(ac\)?MediumLevel 29Which equation has (b=0) and (c>0)?MediumLevel 29How will (\frac{x^2}{4}-x+3=0) be written without fractions?MediumLevel 29What is the equivalent equation with integer coefficients for \(\frac{2}{5}x^2+\frac{1}{5}x-2=0\)?MediumLevel 29Which option is not a quadratic equation in the usual form?MediumLevel 29What is the value of b in \(x^2-4\sqrt{2}x+8=0\)?MediumLevel 29If the roots are -3 and -8, what is the product of the roots?MediumLevel 29Which quadratic equation has sum of roots (-6) and product (8)?MediumLevel 29What is the sum of roots of (4x^2-7x+2=0)?MediumLevel 29What is the product of roots of (5x^2-3x-11=0)?MediumLevel 29If the sum of roots of (3x^2+nx+12=0) is (-4), what is (n)?MediumLevel 29