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
The roots of the equation \(x^2-4x+1=0\) are \(\alpha\) and \(\beta\). What is the value of \(\alpha+\beta+\alpha\beta\)?HardLevel 29If the roots of \\(x^2+px+q=0\\) are 1 and \\(p\\), which relation for \\(q\\) is correct?HardLevel 29Which of the following is a quadratic equation in x but is not written in standard form?HardLevel 29Which equation will have a negative product of roots?HardLevel 29A right triangle has a base of \((x+1)\) units, a height of \((x+3)\) units, and an area of \(30\) square units. Which quadratic equation is obtained from this condition?HardLevel 29If \(\alpha\) and \(\beta\) are the roots of the equation \(x^2+2x-8=0\), what is the value of \((\alpha+\beta)^2\)?HardLevel 29The equation \(x^2+4x+k=0\) has no real roots. What is the correct condition on \(k\)?HardLevel 29If the equation \(x^2-2ax+a^2-9=0\) is given, what is the difference between the larger and smaller roots?HardLevel 29What is the standard quadratic form of ((6x+1)(x-4)=5x)?HardLevel 30If ((n² − 16)x² − 3x + 7 = 0) is a quadratic equation, what is the correct condition on n?MediumLevel 30What is the standard form of the equation \\(2x-3\\)^2+(x+5)^2=34?HardLevel 30Write (\frac{x^2+1}{3}-\frac{x-2}{2}=5) in standard form with integer coefficients.HardLevel 30If (x=-4) is a root of the equation (2x^2+px-12=0), what is the value of (p)?HardLevel 30Which monic quadratic equation has sum of roots (-9) and product (20)?HardLevel 30If the roots of the quadratic equation \(x^2-2kx+25=0\) are equal, what are the possible values of \(k\)?HardLevel 30What condition on \(k\) is necessary for the equation \(x^2+2kx+16=0\) to have real roots?HardLevel 30What is the sum of reciprocals of the roots of (3x^2-10x+7=0)?HardLevel 30If 4 and 5 are the roots of the equation \(x^2-sx+p=0\), what is the value of \(s+p\)?HardLevel 30If the roots of the equation \(x^2-8x+k=0\) are real and distinct, what is the correct condition on \(k\)?HardLevel 30What is the sum of squares of the roots of \(3x^2+8x+4=0\)?HardLevel 30