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Subjects

Mathematics

Methods of Solving Quadratic Equations

द्विघात समीकरणों को हल करने की विधियाँ

In this Class 10 Mathematics topic from the chapter Quadratic Equations, students learn how to find the values of an unknown variable that satisfy a quadratic equation. They practise solving equations by factorisation, completing the square, and using the quadratic formula, while learning when each method is useful. The topic also develops skills in identifying coefficients, calculating the discriminant, checking solutions, and interpreting whether an equation has two, one, or no real roots.

Practice questions

What form is obtained by completing the square in (x^2-2x+5=0)?What are the roots of the equation \(3x^2=12\) when it is solved by the square-root method?When solving (x − 5)² = 3, what is the value of x?Which is the correct solution for (x^2+10x+21=0)?Which is the correct factorised form of the equation \(5x^2+6x+1=0\)?What are the roots of 5x² + 6x + 1 = 0?For which equation is the quadratic formula more convenient than factorisation?What are the roots of (x^2+x-1=0) by the quadratic formula?Which factorised form is correct for (2x^2-3x-2=0)?What are the roots of the quadratic equation \\(2x^2-3x-2=0\\)?If a student wrote only (x=5) from (x^2=25), what is the correction?If x² − 8x + 15 = 0 is solved by completing the square, which middle step is correct?What are the roots obtained by solving \(x^2-8x+15=0\) using the completing-the-square method?Using factorisation method, what will be the roots of (4x^2-12x+5=0)?What is the correct splitting of the middle term in 8x² + 14x + 3 = 0?What are the roots of (8x^2+14x+3=0)?Using the quadratic formula, what roots are obtained for (x^2-8x+12=0)?Which middle step is correct while solving x² − 8x + 12 = 0 by completing the square?What roots are obtained by solving (3x^2+8x+4=0) by factorisation?What is the correct splitting of the middle term in (5x^2-13x-6=0)?