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 the product of roots of (px^2+6x+9=0) is (3), what is the value of (p)?MediumLevel 29In which of the following equations is (x = -2) not a root?MediumLevel 29Which pair is the correct roots of \(x^2+2x-35=0\)?MediumLevel 29If the roots of \(x^2+rx+36=0\) are 6 and 6, what is the value of \(r\)?MediumLevel 29Which quadratic equation is obtained by simplifying \((x-3)^2+2(x-3)-8=0\)?MediumLevel 29What is the standard form of \((x+2)(x-7)=3x\)?MediumLevel 29If \(x^2-12x+35=0\), what is the value of the left-hand side when \(x=5\)?MediumLevel 29If the roots of (x^2-14x+k=0) are equal, what is (k)?MediumLevel 29In (x^2+kx+49=0), if the roots are equal and positive, which possible value of (k) is correct?MediumLevel 29In which option is the (x) term absent but the equation is quadratic?MediumLevel 29If (6x^2-18x+12=0) is divided by (6), which simplified equation is obtained?MediumLevel 29Which pair of integers is useful for factoring the quadratic equation x^2 - 13x + 42 = 0?MediumLevel 29If the quadratic equation \(x^2 + s x + 18 = 0\) has roots \(-3\) and \(-6\), what is the value of \(s\)?MediumLevel 29The area of a square is 15 more than 8 times its side. If the side is x, which equation is correct?MediumLevel 29In which perfect square form can the equation \(x^2+12x+36=0\) be written?MediumLevel 29What is the standard form of ((2x-1)^2=3x+5)?MediumLevel 29If \(x=-4\) is a root of the equation \(x^2+tx-8=0\), what is the value of \(t\)?MediumLevel 29What is the standard quadratic form of \((4x-1)(x+3)=0\)?MediumLevel 30If ((5-p)x^2+2x+9=0) is a quadratic equation, what is the correct condition for (p)?MediumLevel 30For the equation \(6x^2-13x+5=0\), if \(a, b, c\) are the coefficients, what is the value of \(2a+b-c\)?MediumLevel 30