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
What is the difference between the larger and smaller roots of \(5x^2-22x+24=0\)?ExpertLevel 29If the quadratic equation \(x^2-18x+c=0\) can be written as a perfect square, what is the value of \(c\)?ExpertLevel 29If the two roots of the equation \(x^2+bx+100=0\) are equal and each root is \(-10\), what is the value of \(b\)?ExpertLevel 29In which option will the sum of roots be negative and the product of roots be negative?ExpertLevel 29A rectangle has length \(x+9\) units and breadth \(x-6\) units. If its area is 130 square units, which quadratic equation is formed?ExpertLevel 29Two numbers have sum (17) and product (72). They can be roots of which quadratic equation?ExpertLevel 29If (\alpha,\beta) are roots of (x^2-13x+42=0), what is (\frac{1}{\alpha}+\frac{1}{\beta})?ExpertLevel 29If the identity \\((x+a)^2=x^2-20x+100\\) is true for all \\(x\\), what is the value of \\(a\\)?ExpertLevel 29If k is a real number, what is the nature of the roots of the equation 25x² + 40kx + 16k² = 0?ExpertLevel 29If one root of (x^2+mx+49=0) is the reciprocal of the other, what can be said about (m)?ExpertLevel 29The roots of (x^2+px+36=0) are equal and positive. What is the value of (p)?ExpertLevel 29If (x=-2) is not a root of (kx^2+5x+6=0), what condition must (k) satisfy?ExpertLevel 29Which quadratic equation has sum of roots (0) and product (-144)?ExpertLevel 29If in \(5x^2+kx+45=0\), the product of roots is (-3) times the sum of roots, what is (k)?ExpertLevel 29What is the sum of cubes of the roots of (x^2-6x-16=0)?ExpertLevel 29If the roots of the quadratic equation \(x^2+bx+c=0\) are \(-5\) and \(11\), what is the value of \(b+c\)?ExpertLevel 29If a = 3 is substituted, what type of statement does (a − 3)x² + (a² − 9)x + 11 = 0 become?ExpertLevel 29What is the standard form of ((x+5)^2+(x-6)^2=(x+2)^2)?ExpertLevel 29If \(x=-2\) is a root of the equation \(x^2+(5k-2)x+4k=0\), what is the value of \(k\)?ExpertLevel 29The roots of the equation \(x^2-8x+5=0\) are \(\alpha\) and \(\beta\). What is the value of \(\alpha+\beta+4\alpha\beta\)?ExpertLevel 29