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
If (\alpha,\beta) are roots of (x^2-3x+1=0), what is (\alpha^4+\beta^4)?If both roots of the equation \(x^2-12x+m=0\) are prime numbers, what is the value of \(m\)?If (x^2+px+36=0) has equal and positive roots, what is the value of (p)?If (\alpha,\beta) are roots of (3x^2-13x+4=0), what is the positive value of (\alpha-\beta)?If the roots of the equation \(x^2-(2a+7)x+(a+3)(a+4)=0\) are consecutive integers, which pair represents the roots?For (x^2+10x+\lambda=0) to have real distinct roots and both negative roots, what is the correct condition on (\lambda)?If (\alpha,\beta) are roots of (x^2-6x+5=0), what is (\alpha^2-5\alpha+\beta^2-5\beta)?If \(\alpha\) and \(\beta\) are the roots of the equation \(x^2+8x+12=0\), what is the value of \((\alpha-\beta)^2+3\alpha\beta\)?If the roots of the quadratic equation \(x^2+px+q=0\) are \(-3\) and \(7\), what is the value of \(p-q\)?If one root of the equation \(3x^2-(3h+1)x+h=0\) is \(\frac{1}{3}\), what is the other root?What is the nature of the roots of (x^2-2x+(a^2+2)=0)?If (\alpha,\beta) are roots of (x^2-5x+c=0) and (\alpha^2+\beta^2=17), what are the roots?If (x^2+bx+49=0) has equal and negative roots, what is the value of (b)?If \(\alpha\) and \(\beta\) are the roots of the equation \(x^2+x-2=0\), what is the value of \(\alpha^5+\beta^5\)?If the two roots of the equation \(x^2-(u+v+2)x+(u+1)(v+1)=0\) are equal, which of the following statements is correct?If (\alpha,\beta) are roots of (x^2-5x+6=0), which equation has roots (\alpha+\beta) and (\alpha\beta)?What is the positive difference between the two roots of \\(x^2-2kx+k^2-25=0\\)?If the equation \(x^2-2mx+(m^2-m)=0\) has real roots, what is the correct condition on \(m\)?If the sum of the roots of a quadratic equation is 7 and their product is 10, which is its monic quadratic equation?If the roots of a quadratic equation are reciprocals of each other and their sum is (\frac{5}{2}), which equation is possible?