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 the quadratic equation \(x^2+bx+c=0\) are \(-3\) and \(8\), what is the value of \(b+c\)?HardLevel 30Which of the following quadratic equations has one root \(x=0\) and the other root negative?HardLevel 30If \(a=2\), what type of statement does \((a-2)x^2+(a^2-4)x+5=0\) become?HardLevel 30What is the standard form of ((x+2)^2+(x-5)^2=(x+1)^2)?HardLevel 30If \(x=-2\) is a root of the equation \(x^2+(3k+1)x+2k=0\), what is the value of \(k\)?HardLevel 30The roots of the equation \\(x^2-5x+2=0\\) are \\(\\alpha\\) and \\(\\beta\\). What is the value of \\(\\alpha+\\beta+2\\alpha\\beta\\)?HardLevel 30If the roots of (x^2+px+q=0) are (2) and (p), which relation involving (q) is correct?HardLevel 30If (\alpha, \beta) are the roots of the equation (x^2-9x+20=0) , what is the value of (\alpha-4)(\beta-4) ?HardLevel 30A right triangle has a base of (x+2) units and a height of (x+6) units. If its area is 40 square units, which quadratic equation in x is correct?HardLevel 30If \(\alpha\) and \(\beta\) are the roots of the quadratic equation \(x^2-9x+14=0\), what is the value of \((\alpha+\beta)^2\)?HardLevel 30If (\alpha,\beta) are roots of (x^2-4x-21=0), what is (\alpha\beta+2\alpha+2\beta)?HardLevel 30The equation \(x^2+8x+k=0\) has no real roots. What is the correct condition on \(k\)?HardLevel 30If the equation \(x^2-2ax+a^2-16=0\) is given, what is the difference between its roots?HardLevel 30If the roots of (x^2+px+q=0) are (3) and (p), what is a possible value of (p)?HardLevel 30What is the standard form of \((x-2)(x+3)+(2x-1)(x-4)=0\)?HardLevel 30What is the standard quadratic form of ((2x+5)(3x-4)=4(x-1))?ExpertLevel 28If ((k^2-25)x^2+(k-5)x+1=0) is a quadratic equation, what is the correct condition on (k)?ExpertLevel 28What is the standard form \(ax^2+bx+c=0\) of the equation \((x+2)^2+2(x-3)^2=35\)?ExpertLevel 28What is the standard form with integer coefficients of (\frac{2x^2-1}{5}+\frac{x+3}{2}=7)?ExpertLevel 28If \(x=-3\) is a root of the equation \(4x^2+px-9=0\), what is the value of \(p\)?ExpertLevel 28