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 quadratic equation has sum of roots (0) and product (-169)?ExpertLevel 30If in \(6x^2+kx+66=0\), the product of roots is (-2) times the sum of roots, what is (k)?ExpertLevel 30What is the sum of cubes of the roots of (x^2-7x-18=0)?ExpertLevel 30If the roots of \(x^2+bx+c=0\) are \(-6\) and \(13\), what is the value of \(b+c\)?ExpertLevel 30If \(a=-4\), what type of statement does \((a+4)x^2+(a^2-16)x+13=0\) become?ExpertLevel 30What is the standard form of ((x+6)^2+(x-7)^2=(x+3)^2)?ExpertLevel 30If \(x=-1\) is a root of \(x^2+(6k-3)x+5k=0\), what is the value of \(k\)?ExpertLevel 30The roots of \(x^2-9x+4=0\) are \(\alpha,\beta\). What is \(\alpha+\beta+5\alpha\beta\)?ExpertLevel 30If the roots of (x^2+px+q=0) are (6) and (p), what is the value of (p)?ExpertLevel 30If \(\alpha,\beta\) are the roots of \(x^2-20x+96=0\), what is the value of \((\alpha-8)(\beta-8)\)?ExpertLevel 30A right triangle has base \((x+5)\), height \((x+9)\), and area 95 square units. Which quadratic equation represents this situation?ExpertLevel 30If \((\alpha,\beta)\) are the roots of \(x^2-19x+84=0\), what is the value of \((\alpha+\beta)^2\)?ExpertLevel 30The equation \(x^2+14x+k=0\) has no real roots. What is the correct condition on \(k\)?ExpertLevel 30If \(x^2-2ax+a^2-49=0\), what is the difference between the two roots of this quadratic equation?ExpertLevel 30What is the standard quadratic form of (\frac{x+3}{x-2}+\frac{x-2}{x+3}=\frac{13}{6})?ExpertLevel 30If (\alpha,\beta) are roots of (3x^2-11x+6=0), what is the value of (\frac{\alpha}{\beta}+\frac{\beta}{\alpha})?ExpertLevel 30If the roots of (x^2-(2k+5)x+(k^2+5k+6)=0) are consecutive integers, what will those roots be?ExpertLevel 30If the roots of \(x^2+px+q=0\) are \(p+2\) and \(q-2\), and \(p+q=8\), what is the value of \(p\)?ExpertLevel 30