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
If (\alpha,\beta) are roots of (7x^2-25x+12=0), what is (\alpha\beta)?If \(\alpha,\beta\) are roots of \(7x^2-25x+12=0\), what is \((\alpha-\beta)^2\)?If (x^2-14x+n=0) has no real roots, which condition on (n) is correct?If (x^2-14x+n=0) has two distinct real roots, which condition on (n) is correct?Which factorised form of the equation \(7x^2-19x-6=0\) is correct for solving it?What are the roots of the equation \(7x^2-19x-6=0\)?If (x^2+12x+8=0), which form is correct by completing square?What are the roots of the equation \(x^2+12x+8=0\)?If the roots of (x^2-10x-24=0) are (\alpha,\beta), what is (\alpha^2\beta+\alpha\beta^2)?If one root of (x^2+px+49=0) is double the other and both are negative, what is (p)?What is the difference between the roots of (x^2-11x+6=0)?What is the correct statement about real roots of (6x^2-12x+17=0)?Which completed square form is correct for (6x^2-12x+17=0)?If roots of (x^2-14x+33=0) are (\alpha,\beta), which equation has roots (\alpha+5,\beta+5)?If the roots of (x^2-22x+117=0) are (\alpha,\beta), what is (\frac{\alpha}{\beta}+\frac{\beta}{\alpha})?If the quadratic equation \(kx^2-22x+121=0\) has equal roots, what is the value of \(k\)?What is (k) for equal roots of (x^2-2(k+6)x+k^2=0)?If ((x-6)(x-13)=0), what are the solutions by zero product rule?If ((x-6)(x-13)=22), what is the standard quadratic equation?What are the roots of (x^2-19x+56=0) by quadratic formula?