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 (-8) and product (15)?MediumLevel 30What is the sum of roots of (5x^2-9x+4=0)?MediumLevel 30If the sum of roots of (4x^2+mx+20=0) is (-6), what is (m)?MediumLevel 30If the product of roots of (qx^2-8x+12=0) is (4), what is the value of (q)?MediumLevel 30Which pair of roots is correct for the equation \(x^2-3x-40=0\)?MediumLevel 30If both roots of the equation \(x^2 + u x + 64 = 0\) are 8, what is the value of \(u\)?MediumLevel 30Which quadratic equation is obtained by simplifying \((x+4)^2 - 3(x+4) - 10 = 0\)?MediumLevel 30Which equation is obtained when \((x-4)(x+9)=5x\) is written in standard form?MediumLevel 30What is the value of the left-hand side of the quadratic equation \(x^2-15x+56=0\) when \(x=7\) is substituted?MediumLevel 30If the roots of (x^2-18x+k=0) are equal, what is (k)?MediumLevel 30In (x^2+kx+81=0), if the roots are equal and negative, which possible value of (k) is correct?MediumLevel 30In which option is the constant term absent but the equation is quadratic?MediumLevel 30If (8x^2-32x+24=0) is divided by (8), which simplified equation is obtained?MediumLevel 30To factorise the quadratic equation \(x^2-17x+72=0\), which two numbers should have a sum of 17 and a product of 72?MediumLevel 30If the roots of the equation \(x^2+vx+28=0\) are \(-4\) and \(-7\), what is the value of \(v\)?MediumLevel 30The area of a square is 21 more than 10 times its side. If the side of the square is \(x\), which quadratic equation is obtained?MediumLevel 30Which of the following is the perfect-square form of the equation \(x^2-18x+81=0\)?MediumLevel 30Which equation is obtained when \((3x+4)^2=7x+16\) is written in standard quadratic form?MediumLevel 30If 4 is a root of the equation \(x^2+sx-32=0\), what is the value of \(s\)?MediumLevel 30What is the value of (b^2+ac) in (7x^2-5x+2=0)?MediumLevel 30