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 (\alpha,\beta) are roots of (x^2-10x+q=0) and (\alpha^2+\beta^2=58), what is the value of (q)?ExpertLevel 28The length of a rectangle is \\(2x+1\\) units and its breadth is \\(x-4\\) units. If its area is \\(45\\) square units, which quadratic equation represents this situation?ExpertLevel 28What is the standard quadratic form of ((3x-2)(2x+5)=4(x+1))?ExpertLevel 29If ((r^2-49)x^2+(r+7)x+2=0) is a quadratic equation, what is the correct condition on (r)?ExpertLevel 29What is the standard form of the equation 2(x−1)² + 3(x+2)² = 65?ExpertLevel 29What is the standard form with integer coefficients of (\frac{3x^2+2}{4}-\frac{x-5}{3}=6)?ExpertLevel 29If \(x=-5\) is a root of the equation \(3x^2+px-20=0\), what is the value of \(p\)?ExpertLevel 29Which monic quadratic equation has sum of roots (-13) and product (42)?ExpertLevel 29If the two roots of the quadratic equation \(x^2-2mx+49=0\) are equal, what are the possible values of \(m\)?ExpertLevel 29What condition on \(p\) is necessary and sufficient for the equation \(x^2+2px+36=0\) to have real roots?ExpertLevel 29What is the sum of reciprocals of the roots of (5x^2-17x+6=0)?ExpertLevel 29If 7 and 8 are the roots of the equation \(x^2-sx+p=0\), what is the value of \(s+p\)?ExpertLevel 29If the roots of the equation \(x^2-16x+k=0\) are real and distinct, what is the correct condition on \(k\)?ExpertLevel 29Which quadratic equation has a discriminant of −35?ExpertLevel 29What is the sum of squares of the roots of (4x^2+8x+3=0)?ExpertLevel 29If \(\alpha\) and \(\beta\) are the roots of the equation \(x^2-14x+48=0\), what is the value of \((\alpha-6)(\beta-6)\)?ExpertLevel 29What is the standard form of the equation (x+4)(x+7)+(x−3)(x+6)=88?ExpertLevel 29If the roots of a monic quadratic equation are (2r) and (5r), and their sum is (21), what will be the constant term?ExpertLevel 29Which statement correctly describes the nature of the roots of \(x^2-10x+29=0\)?ExpertLevel 29Which of the following becomes a quadratic equation in the variable \(x\) after simplification?ExpertLevel 29