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
If the roots of (x^2+px+q=0) are (5) and (p), what is the value of (p)?ExpertLevel 29If \(\alpha\) and \(\beta\) are the roots of the quadratic equation \(x^2-16x+63=0\), what is the value of \((\alpha-7)(\beta-7)\)?ExpertLevel 29A right triangle has a base of (x+4) units, a height of (x+8) units, and an area of 72 square units. Which quadratic equation is formed from this information?ExpertLevel 29If \(\alpha\) and \(\beta\) are the roots of the quadratic equation \(x^2-15x+44=0\), what is the value of \((\alpha+\beta)^2\)?ExpertLevel 29After simplification, which of the following equations does not remain a quadratic equation in x?ExpertLevel 29If the equation \(x^2-2ax+a^2-36=0\) is given, what is the difference between its larger and smaller roots?ExpertLevel 29What is the standard quadratic form of (x + 2)/(x − 1) + (x − 1)/(x + 2) = 5/2?HardLevel 29If (\alpha,\beta) are roots of (2x^2-7x+3=0), what is the value of (\frac{\alpha}{\beta}+\frac{\beta}{\alpha})?ExpertLevel 29If the roots of (x^2-(2k+3)x+(k^2+3k)=0) are consecutive positive integers, what is the value of (k)?ExpertLevel 29If roots of (x^2+px+q=0) are (p+1) and (q-1), and (p+q=5), what is the value of (pq)?ExpertLevel 29What is the standard quadratic form of ((4x-3)(x+5)=2(3x-1))?ExpertLevel 30If ((t^2-64)x^2+(t-8)x+5=0) is a quadratic equation, what is the correct condition on (t)?ExpertLevel 30What is the standard form of the equation \(3(x+1)^2+2(x-4)^2=74\)?ExpertLevel 30What is the standard form with integer coefficients of (\frac{4x^2-3}{5}+\frac{x-2}{4}=3)?ExpertLevel 30If \(x=-6\) is a root of \(2x^2+px-18=0\), what is the value of \(p\)?ExpertLevel 30Which monic quadratic equation has sum of roots (-15) and product (56)?ExpertLevel 30If the roots of \(x^2-2mx+64=0\) are equal, what are the possible values of \(m\)?ExpertLevel 30What is the condition on p for the equation \(x^2+2px+49=0\) to have real roots?ExpertLevel 30What is the sum of reciprocals of the roots of (6x^2-19x+10=0)?ExpertLevel 30If 8 and 9 are the roots of the equation \(x^2 - s x + p = 0\), what is the value of \(s+p\)?ExpertLevel 30