List of top Mathematics Questions on Relationship between Zeroes and Coefficients of a Polynomial

If the zeroes of a polynomial p(x) are $-3$ and 8, then p(x) equals

If sum and product of zeroes of a polynomial are ($-3$) and ($-2$) respectively, then a polynomial is

If the zeroes of a polynomial $p(x)$ are $-3$ and $8$, then $p(x)$ equals

\(\alpha\) and \(\beta\) are the zeroes of the polynomial \(5x^2 - 16x - 10\). Find the value of \(\frac{\alpha}{\beta} + \frac{\beta}{\alpha}\).

\(\alpha, \beta\) are zeroes of the polynomial p(x) = 3x\(^2\) – 6x – 5. Find the value of \(\frac{1}{\alpha^2} + \frac{1}{\beta^2}\).

\(\alpha\) and \(\beta\) are the zeroes of the polynomial \(5x^2 - 16x - 10\). Find the value of \(\frac{\alpha}{\beta} + \frac{\beta}{\alpha}\).

Find the quadratic polynomial the sum of whose zeroes is 1 and their product is –12. Hence find the zeroes of the polynomial.

Find a quadratic polynomial whose zeroes are $(5 - 2\sqrt{3})$ and $(5 + 2\sqrt{3})$.

The sum and product of zeroes of a quadratic polynomial $p(x)$ are $-\frac{1}{3}$ and $2$ respectively. The polynomial $p(x)$ is :

If \(\alpha\), \(\beta\) are the zeroes of the quadratic polynomial \(px^2 + qx + r\), then find the value of \(\alpha^3\beta + \beta^3\alpha\).

If \(\alpha\) and \(\beta\) are two zeroes of a polynomial \(f(x) = px^2 - 2x + 3p\) and \(\alpha + \beta = \alpha\beta\), then value of p is :

Find the zeroes of the quadratic polynomial $x^2 + 7x + 10$, and verify the relationship between the zeroes and its coefficients.

If $\alpha, \beta$ are the zeroes of the polynomial $p(x) = x^2 - 3x - 1$, then find the value of $\frac{1}{\alpha} + \frac{1}{\beta}$.

If the zeroes of the polynomial \(p(x) = 2x^2 - 7x + 6\) are \(\alpha\) and \(\beta\), then the value of \(\frac{1}{\alpha} + \frac{1}{\beta}\) is

The value of k for which sum of the zeroes of the polynomial \(p(x) = 3x^2 - kx + 6\) is 2, is