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 equation \(x^2-9x+20=0\) is given and \(x=4\) is substituted, what value does the left-hand side take?MediumLevel 28Which equation will have roots that are opposite numbers?MediumLevel 28In (x^2+kx+25=0), if the roots are equal and negative, which possible value of (k) is correct?MediumLevel 28In which option is the (x) term absent but the equation is still quadratic?MediumLevel 28If (3x^2-12x+12=0) is divided by (3), which simplified equation is obtained?MediumLevel 28Which pair of numbers helps determine the roots of the equation \(x^2-11x+30=0\)?MediumLevel 28If the roots of \(x^2+ax+10=0\) are \(-2\) and \(-5\), what is the value of \(a\)?MediumLevel 28The area of a square is 7 more than 6 times its side. If the side is \(x\), which equation is correct?MediumLevel 28The equation \(x^2-4x+4=0\) can be written in which perfect-square form?MediumLevel 28What is the standard form of ((x+3)^2=2x+15)?MediumLevel 28What is the standard quadratic form of \((3x+2)(x-5)=0\)?MediumLevel 29If ((2m-3)x^2+7x-1=0) is a quadratic equation, what is the correct condition for (m)?MediumLevel 29For the equation -4x^2 + 6x - 9 = 0, what is the value of a - b + c?MediumLevel 29What is the standard form of 8x − x² = 15 with a positive coefficient of x²?MediumLevel 29Is \(x=-1\) a root of the equation \(x^2+5x+4=0\)?MediumLevel 29If \(x=3\) is a root of the equation \(2x^2+qx-15=0\), what is the value of \(q\)?MediumLevel 29Which equation is quadratic but not yet in standard form?MediumLevel 29What is the standard form of ((x+4)^2=5x+10)?MediumLevel 29If (a=5), (b=-11), (c=-6), which is the corresponding quadratic equation?MediumLevel 29What is the discriminant \(D\) of the equation \(9x^2-12x+4=0\)?MediumLevel 29