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 roots of \(x^2-20x+k=0\) are real and distinct, what is the correct condition on \(k\)?ExpertLevel 30Which of the following quadratic equations has discriminant -47?ExpertLevel 30What is the sum of squares of the roots of \(6x^2+7x+2=0\)?ExpertLevel 30If \(\alpha\) and \(\beta\) are the roots of \(x^2-18x+80=0\), what is the value of \((\alpha-8)(\beta-8)\)?ExpertLevel 30What is the standard form of ((x+5)(x+8)+(x-4)(x+7)=110)?ExpertLevel 30If the roots of a monic quadratic equation are (3r) and (4r), and their sum is (28), what will be the constant term?ExpertLevel 30Which of the following statements is true for the equation \(x^2 - 12x + 40 = 0\)?ExpertLevel 30If one root of the quadratic equation \(x^2-(m+7)x+7m=0\) is 7, what is the other root?ExpertLevel 30What is the difference between the roots of the equation \(7x^{2}-30x+32=0\)?ExpertLevel 30If \(x^2+24x+c=0\) is a perfect-square quadratic, what is the value of \(c\)?ExpertLevel 30If both roots of \(x^2+bx+144=0\) are equal and each is \(-12\), what is the value of \(b\)?ExpertLevel 30In which option will the sum of roots be positive and the product of roots be positive?ExpertLevel 30A rectangle has length \((x+10)\) and breadth \((x-7)\). If its area is \(160\), which equation is correct?ExpertLevel 30Two numbers have sum (19) and product (90). They can be roots of which quadratic equation?ExpertLevel 30If (\alpha,\beta) are roots of (x^2-17x+72=0), what is (\frac{1}{\alpha}+\frac{1}{\beta})?ExpertLevel 30If \((x+a)^2 = x^2 + 28x + 196\), what is the value of \(a\)?ExpertLevel 30What is the nature of the roots of the quadratic equation \(36x^2-60kx+25k^2=0\)?ExpertLevel 30If one root of (x^2+mx+64=0) is the reciprocal of the other, what can be said about (m)?ExpertLevel 30The roots of (x^2+px+49=0) are equal and negative. What is the value of (p)?ExpertLevel 30If (x=3) is not a root of (kx^2-8x+5=0), what condition must (k) satisfy?ExpertLevel 30