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 monic quadratic equation has sum of roots (-11) and product (30)?ExpertLevel 28If the roots of the quadratic equation \(x^2-2mx+36=0\) are equal, what are the possible values of \(m\)?ExpertLevel 28If \(p\) is a real number, what is the condition for the equation \(x^2+2px+25=0\) to have real roots?ExpertLevel 28What is the sum of reciprocals of the roots of (4x^2-13x+9=0)?ExpertLevel 28If 5 and 6 are the roots of the equation \(x^2-sx+p=0\), what is the value of \(s+p\)?ExpertLevel 28If the roots of the equation \(x^2-12x+k=0\) are real and distinct, what is the correct condition on \(k\)?ExpertLevel 28Which of the following quadratic equations has roots that are reciprocals of each other?ExpertLevel 28What is the sum of squares of the roots of \(5x^2+6x+1=0\)?ExpertLevel 28If (\alpha) and (\beta) are the roots of the equation (x^2-9x+18=0), what is the value of ((\alpha-3)(\beta-3))?ExpertLevel 28Which of the following is a quadratic equation, even though it has terms involving the variable on both sides?ExpertLevel 28Which statement correctly describes the nature of the roots of \(x^2-8x+17=0\)?ExpertLevel 28If one root of the equation \(x^2-(m+5)x+5m=0\) is \(5\), what is the other root?ExpertLevel 28What is the absolute difference between the roots of \(3x^2-14x+16=0\)?ExpertLevel 28Which condition is essential for an equation of the form \(ax^2+bx+c=0\) to be called a quadratic equation?ExpertLevel 28If both roots of the quadratic equation \\(x^2+bx+64=0\\) are equal and each root is \\(-8\\), what is the value of \\(b\\)?ExpertLevel 28In which option will the sum of roots be positive and the product of roots be negative?ExpertLevel 28A rectangle has length \((x+8)\) and breadth \((x-5)\). If its area is \(104\) square units, which quadratic equation correctly represents this situation?ExpertLevel 28Two numbers have sum (15) and product (54). They can be roots of which quadratic equation?ExpertLevel 28If (\alpha,\beta) are roots of (x^2-11x+30=0), what is (\frac{1}{\alpha}+\frac{1}{\beta})?ExpertLevel 28If \\(x+a\\)^2=x^2+18x+81 is an identity, what is the value of \\(a\\)?ExpertLevel 28