Mathematics
Roots of a Quadratic Equation
द्विघात समीकरण के मूल
Roots of a Quadratic Equation, taught in Class 10 Mathematics under the chapter Quadratic Equations, introduces the values of the variable that make a quadratic expression equal to zero. Students learn to identify roots, verify them by substitution, and connect the sum and product of the roots with the coefficients. The topic also helps them form a quadratic equation when its roots are known and use these relationships to solve and check mathematical problems.
Practice questions
Which is the correct pair of roots of (x^2+3x-18=0)?If (x^2-sx+9=0) has equal and positive roots, what is (s)?If ((k-2)x^2+4x+1=0) has equal roots, what is the value of (k)?If (\alpha,\beta) are roots of (x^2-6x+8=0), what is ((\alpha-2)(\beta-2))?If the difference between the roots of (3x^2-11x+p=0) is (\frac{5}{3}), what is the value of (p)?If (x^2-2(k+2)x+k^2+5=0) has equal roots, what is the value of (k)?If (α,β) are the roots of (x^2-6x+5=0), which equation has roots (3α-2) and (3β-2)?If the roots of (2x^2+mx+8=0) are in the ratio (1:2), what are the possible values of (m)?Which statement is always true for (x^2-(a+4)x+4a=0)?If (\alpha,\beta) are the roots of (x^2-5x+2=0), what is (\frac{1}{\alpha^2}+\frac{1}{\beta^2})?If the roots of (kx^2-8x+k=0) are real and reciprocal, what is the correct condition on (k)?If the roots of (x^2+px+12=0) are (r) and (r+1), what are the possible values of (p)?For the equation \(4x^2-4(a-1)x+a^2-4a=0\) to have real roots, what is the correct condition on \(a\)?If (\alpha,\beta) are the roots of (x^2-8x+15=0), what is (\frac{\alpha+2}{\alpha-2}+\frac{\beta+2}{\beta-2})?If (\alpha,\beta) are the roots of (x^2-7x+10=0), what is (\frac{\alpha+2}{\alpha-2}+\frac{\beta+2}{\beta-2})?If (\alpha,\beta) are the roots of (2x^2-5x+3=0), what is (\alpha^3+\beta^3)?If the two roots of the quadratic equation \(x^2+(m-5)x+9=0\) are equal and not of opposite signs, what are the possible values of \(m\)?If the roots of the equation \(x^2+ax+b=0\) are \(2+\sqrt{3}\) and \(2-\sqrt{3}\), what is the value of \(a+b\)?If (\alpha,\beta) are the roots of (x^2-3x-1=0), what is (\alpha^2+3\beta+\alpha\beta) when (\alpha) is the larger root?If (\alpha,\beta) are the roots of (x^2-3x-1=0), what is the correct value of (\alpha^2+3\beta+\alpha\beta)?