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
Which equation will have sum of roots (0)?MediumLevel 30The base and height of a right triangle are \(x\) cm and \(x+2\) cm, respectively. If its area is \(24\text{ cm}^2\), which quadratic equation in \(x\) is correct?MediumLevel 30What is the standard quadratic form of ((5x-2)(2x+3)=7x)?HardLevel 29If (m² − 9)x² + 4x − 5 = 0 is a quadratic equation, what is the correct condition on m?HardLevel 29When the equation (x-2)^2+(2x+1)^2=25 is written in the standard quadratic form ax^2+bx+c=0, which form is obtained?HardLevel 29Write (\frac{x^2-3}{2}+\frac{x-1}{3}=4) in standard form with integer coefficients.HardLevel 29If \\(x=-2\\) is a root of the equation \\(3x^2+px+10=0\\), what is the value of \\(p\\)?HardLevel 29Which monic quadratic equation has a sum of roots equal to 7 and a product of roots equal to 10?HardLevel 29If the two roots of the equation \(x^2-2kx+16=0\) are equal, what are the possible values of \(k\)?HardLevel 29What condition on \(k\) is necessary and sufficient for the equation \(x^2+2kx+9=0\) to have real roots?HardLevel 29What is the sum of reciprocals of the roots of (2x^2-5x+3=0)?HardLevel 29If 2 and 3 are the roots of the equation \(x^2-sx+p=0\), what is the value of \(s+p\)?HardLevel 29If the roots of the equation \(x^2-6x+k=0\) are real and distinct, what is the correct condition on \(k\)?HardLevel 29What is the sum of squares of the roots of \(2x^2+7x+3=0\)?HardLevel 29If \(\alpha\) and \(\beta\) are the roots of the quadratic equation \(x^2-8x+15=0\), what is the value of \((\alpha-1)(\beta-1)\)?HardLevel 29In which option will the given equation not remain quadratic?HardLevel 29What is the standard form of the equation \((x+1)(x+2)+(x+3)(x+4)=50\)?HardLevel 29If the roots of (x^2+px+q=0) are (p) and (q) themselves, which relation is correct?HardLevel 29Which statement correctly describes the nature of the roots of the quadratic equation \(x^2-4x+6=0\)?HardLevel 29If one root of the equation \(x^2-(m+2)x+2m=0\) is \(2\), what is the other root?HardLevel 29