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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

For (\frac{1}{x}+x=\frac{10}{3}), (x\neq0), what quadratic form is obtained?What are the solutions of (\frac{1}{x}+x=\frac{10}{3}), (x\neq0)?What is the correct quadratic form of (\frac{x+2}{x}=\frac{9}{x+2}), (x\neq0,-2)?What are the solutions of (\frac{x+2}{x}=\frac{9}{x+2}), (x\neq0,-2)?What are the roots of (x^2-6x+2=0) by quadratic formula?If the sum of roots of (4x^2+px+16=0) is (-6), what is (p)?If the product of roots of (5x^2-11x+p=0) is (\frac{2}{5}), what is (p)?If the roots of (x^2-13x+40=0) are (\alpha) and (\beta), what is (\alpha^2+\beta^2)?If the roots of (x^2-9x+20=0) are (\alpha) and (\beta), what is (\frac{1}{\alpha}+\frac{1}{\beta})?If (\alpha,\beta) are roots of (3x^2-11x+6=0), what is (\alpha+\beta)?If (\alpha,\beta) are roots of (3x^2-11x+6=0), what is (\alpha\beta)?If \(\alpha,\beta\) are roots of \(3x^2-11x+6=0\), what is \((\alpha-\beta)^2\)?If (x^2-8x+n=0) has no real roots, which condition on (n) is correct?If (x^2-8x+n=0) has two distinct real roots, which condition on (n) is correct?Which of the following is the correct factorised form for solving the equation 3x² − 5x − 2 = 0?What are the roots of the equation \(3x^2-5x-2=0\)?If x² + 6x + 2 = 0, which form is correct by completing the square?What are the roots of the equation \(x^2+6x+2=0\)?If the roots of (x^2-4x-12=0) are (\alpha,\beta), what is (\alpha^2\beta+\alpha\beta^2)?If one root of (x^2+px+16=0) is double the other and both are negative, what is (p)?