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
When the equation \(12-7x+x^2=0\) is written in standard form \(ax^2+bx+c=0\), what is the value of \(b\)?MediumLevel 30Is \(x=5\) a root of the equation \(x^2-6x+5=0\)?MediumLevel 30Write the equation \((x-6)^2 = 4x + 5\) in its standard form \(ax^2+bx+c=0\).MediumLevel 30If a = −2, b = 9 and c = −7, which is the corresponding quadratic equation?EasyLevel 30What is the discriminant \(D\) of the equation \(25x^2-20x+4=0\)?MediumLevel 30What is the nature of the roots of the equation \(x^2+14x+49=0\)?MediumLevel 30What is the sign of the discriminant of the equation \(4x^2+x+6=0\)?MediumLevel 30If the roots of a quadratic are \(-5\) and \(4\), what is the monic quadratic equation?MediumLevel 30When nine times a number x is subtracted from its square, the result is 36. Which equation correctly represents this?MediumLevel 30The sum of the squares of two consecutive positive integers is 145. If the smaller integer is \(x\), which equation is correct?MediumLevel 30The length of a rectangle is 7 units more than its breadth, and its area is 120 square units. If the breadth is \(x\) units, which quadratic equation is formed in \(x\)?MediumLevel 30What are the roots of the equation \(x^2 - 10x = 0\)?MediumLevel 30What are the roots of (49x^2-64=0)?MediumLevel 30Which factored form represents the equation \(x^2+11x+30=0\)?MediumLevel 30What is the value of \(ac\) in the equation \(4x^2+13x+3=0\)?MediumLevel 30How will (\frac{x^2}{5}+2x-7=0) be written without fractions?MediumLevel 30Which of the following is the equivalent equation with integer coefficients for \(\frac{3}{4}x^2-\frac{1}{2}x+2=0\)?MediumLevel 30Which option is not a usual quadratic equation?MediumLevel 30What is the value of \(b\) in the equation \(x^2+6\sqrt{5}\,x+45=0\)?MediumLevel 30If the roots are \\(-4\\) and \\(-9\\), what is the product of the roots?MediumLevel 30