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^2-5x+1=0), what is (\alpha^4+\beta^4)?ExpertLevel 33If both roots of (x^2-14x+m=0) are prime numbers, what is the sum of possible values of (m)?ExpertLevel 33If (x^2+px+64=0) has equal and positive roots, what is the value of (p)?ExpertLevel 33If (\alpha,\beta) are roots of (4x^2-20x+9=0), what is the positive value of (\alpha-\beta)?ExpertLevel 33If (\alpha,\beta) are roots of (4x^2-20x+9=0), what is the correct positive value of (\alpha-\beta)?ExpertLevel 33Which of the following quadratic equations has real, distinct, and irrational roots?ExpertLevel 33For (x^2+12x+\lambda=0) to have real distinct roots and both negative roots, what is the correct condition on (\lambda)?ExpertLevel 33If (\alpha,\beta) are roots of (x^2-7x+10=0), what is (\alpha^2-6\alpha+\beta^2-6\beta)?ExpertLevel 33If (\alpha,\beta) are roots of (x^2-7x+10=0), what is the correct value of (\alpha^2-6\alpha+\beta^2-6\beta)?ExpertLevel 33If (\alpha,\beta) are roots of (x^2+10x+21=0), what is ((\alpha-\beta)^2+4\alpha\beta)?ExpertLevel 33If the roots of \\(x^2+px+q=0\\) are \\(-4\\) and \\(9\\), what is the value of \\(p-q\\)?ExpertLevel 33If one root of the equation \(4x^2-(4h+1)x+h=0\) is \(\frac{1}{4}\), what is the other root?ExpertLevel 33What is the nature of the roots of (x^2-2x+(a^2+3)=0)?ExpertLevel 33If (\alpha,\beta) are roots of (x^2-6x+c=0) and (\alpha^2+\beta^2=26), what are the roots?ExpertLevel 33If \(\alpha\) and \(\beta\) are the roots of the equation \(x^2+x-6=0\), what is the value of \(\alpha^5+\beta^5\)?ExpertLevel 33If (\alpha,\beta) are the roots of (x^2-(2a+1)x+a^2+a-6=0), what is the positive value of (\alpha-\beta)?ExpertLevel 33What are the roots of x² − 16x = 0?EasyLevel 34If x² − 5x = 0 is divided by x and only x − 5 = 0 is written, which root is missed?EasyLevel 35What are the roots of 7x² + 8x + 1 = 0?MediumLevel 35