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 positive difference between the roots of the equation \(3x^2-10x+8=0\)?HardLevel 29If the equation \(x^2+6x+c=0\) is a perfect-square quadratic equation, what is the value of \(c\)?HardLevel 29If both roots of the quadratic equation \(x^2+bx+25=0\) are equal and each root is \(-5\), what is the value of \(b\)?HardLevel 29In which option will both the sum and product of roots be positive?HardLevel 29A rectangle has length ((x+5)) and breadth ((x-2)). If its area is 84, which quadratic equation correctly represents this situation?HardLevel 29Two numbers have sum (11) and product (30). They can be roots of which quadratic equation?HardLevel 29If (\alpha,\beta) are roots of (x^2-5x+6=0), what is (\frac{1}{\alpha}+\frac{1}{\beta})?HardLevel 29Which of the following quadratic equations has two equal and positive roots?HardLevel 29If \\(x+a)^2=x^2+10x+25\\) is an identity, what is the value of \\(a\\)?HardLevel 29If \(k\) is a real constant, what is the nature of the roots of the equation \(4x^2-4kx+k^2=0\)?HardLevel 29If one root of (x^2+mx+16=0) is the reciprocal of the other, what can be said about (m)?HardLevel 29The roots of (x^2+px+9=0) are equal and negative. What is the value of (p)?HardLevel 29Which quadratic equation has sum of roots (0) and product (-49)?HardLevel 29If in \(2x^2+kx+18=0\), the product of roots is (-3) times the sum of roots, what is (k)?HardLevel 29What is the sum of cubes of the roots of (x^2-2x-3=0)?HardLevel 29If the roots of \\(x^2+bx+c=0\\) are \\(-2\\) and \\(7\\), what is the value of \\(b+c\\)?HardLevel 29Which of the following quadratic equations has one root \(x=0\) and the other root positive?HardLevel 29If \\(a=-1\\) is substituted in the equation \\((a+1)x^2+(a^2-1)x+2=0\\), what type of result is obtained?HardLevel 29What is the standard form of ((x-1)^2+(x-2)^2=(x-3)^2)?HardLevel 29If \(x=1\) is a root of the quadratic equation \(x^2+(2k-1)x+k=0\), what is the value of \(k\)?HardLevel 29