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 the roots of x^2+px+25=0 are equal and both negative, what is the value of p?If one root of (x^2+ax+a=0) is (2), what will be the other root?If the difference between the roots of x² - 7x + q = 0 is 1, what is the value of q?If (\alpha) and (\beta) are roots of (x^2-Sx+P=0), what is ((\alpha-\beta)^2) equal to?If 1 is added to each root of the equation \(x^2-6x-16=0\), which monic equation is formed from the resulting roots?If 2 is subtracted from each root of the equation \(x^2-6x-16=0\), what is the product of the resulting roots?If α and β are roots of x^2-4x+3=0, which equation has 3α and 3β as roots?If 8\alpha9 and 8\beta9 are the roots of 8x^2-6x+5=09, what is the sum of 8\alpha+39 and 8\beta+39?If () and () are the roots of (x^2-12x+36=0), what is the value of (-)?If α and β are roots of x^2+4x-21=0, what is the value of |α-β|?If the sum of roots is (6) and the sum of their squares is (52), what is the product of roots?If the roots of the equation \(x^2-9x+c=0\) are in the ratio \(1:2\), what is the value of \(c\)?If the roots of the equation \(x^2+px+18=0\) are in the ratio \(1:2\) and both roots are negative, what is the value of \(p\)?For the quadratic equation \(ax^2+bx+c=0\), where \(a\ne0\), when will its roots be reciprocals of each other?If the product of roots of (4x^2-3x+k=0) equals the sum of roots, what is (k)?If the quadratic equation \(x^2-4x+(m+4)=0\) has no real roots, which condition on \(m\) is correct?If the two roots of the equation \(x^2-2(m+2)x+(m+2)^2=0\) are equal, which statement about \(m\) is correct?If \(\alpha\) and \(\beta\) are the roots of the quadratic equation \(x^2-9x+18=0\), what is the value of \((\alpha-2)(\beta-2)\)?If the roots of the quadratic equation \(5x^2+px+q=0\) are \(3\) and \(-4\), what is the value of \(\frac{q}{5}\)?If the roots of the equation \(x^2+px+q=0\) are \(5\) and \(-2\), what is the value of \(p-q\)?