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 \(\alpha\) and \(\beta\) are the roots of the equation \(x^2+7x+10=0\), what is the value of \((\alpha+2)(\beta+2)\)?HardLevel 30What is the standard form ax^2+bx+c=0) of the equation (x+2)(x+5)+(x-1)(x+4)=609?HardLevel 30Which of the following statements is correct for the equation \\(x^2-6x+11=0\\)?HardLevel 30If one root of the equation \(x^2-(m+4)x+4m=0\) is \(4\), what is the other root?HardLevel 30What is the difference between the roots of the equation \(2x^2-9x+10=0\), taking the larger root minus the smaller root?HardLevel 30If \(x^2-14x+c=0\) is a perfect-square quadratic equation, what is the value of \(c\)?HardLevel 30If the two roots of the quadratic equation \(x^2+bx+49=0\) are equal and each root is \(-7\), what is the value of \(b\)?HardLevel 30In which option will the sum of roots be negative and the product of roots be positive?HardLevel 30Which of the following is a quadratic equation in one variable?HardLevel 30Two numbers have sum (13) and product (40). They can be roots of which quadratic equation?HardLevel 30If (\alpha,\beta) are roots of (x^2-7x+12=0), what is (\frac{1}{\alpha}+\frac{1}{\beta})?HardLevel 30Which of the following quadratic equations will have two equal and negative roots?HardLevel 30If \\(x+a\\)^2 = x^2 - 12x + 36 holds for all real x, what is the value of a?HardLevel 30If \(k\) is a real constant, what is the nature of the roots of the equation \(9x^2+12kx+4k^2=0\)?HardLevel 30If one root of (x^2+mx+25=0) is the reciprocal of the other, what can be said about (m)?HardLevel 30The roots of (x^2+px+16=0) are equal and positive. What is the value of (p)?HardLevel 30If (x=-1) is not a root of (kx^2+3x+2=0), what condition must (k) satisfy?HardLevel 30Which quadratic equation has sum of roots (0) and product (-81)?HardLevel 30If in \(3x^2+kx+12=0\), the product of roots is (-2) times the sum of roots, what is (k)?HardLevel 30What is the sum of cubes of the roots of (x^2-3x-10=0)?HardLevel 30