J P Mohindru and Bharat Mohindru Solutions for Chapter: Polynomials, Exercise 2: EXERCISE

Find a cubic polynomial with the given numbers as the sum, sum of the product of its zeroes taken two at a time, and product of its zeroes respectively.

$0$, $-19$, $30$

Find a cubic polynomial with the given numbers as the sum, sum of the product of its zeroes taken two at a time, and product of its zeroes respectively.

$-3$, $-\frac{1}{4}$, $\frac{3}{4}$

Find the zeroes of $p\left(x\right)=9x^3-x$ and hence verify the relationship between its zeroes and coefficients.

If the zeroes of the cubic polynomial $x^3+3x^2+kx-3$ are $\alpha -\beta$, $\alpha$, $\alpha +\beta$, then find the values of $\alpha$, $\beta$ and $k$.

If $\alpha$, $\beta$, $\gamma$ are the zeroes of the cubic polynomial $p\left(x\right)=7x^3-21x^2+24x+5$ then find the value of ${\alpha }^{-1}+{\beta }^{-1}+{\gamma }^{-1}$.

If $\alpha$, $\beta$, $\gamma$ are the zeroes of the cubic polynomial $p\left(x\right)=7x^3-21x^2+24x+5$ then, find the value of ${\alpha }^2+{\beta }^2+{\gamma }^2$.

If $\alpha$, $\beta$, $\gamma$ are the zeroes of $f\left(x\right)=x^3-5x^2+7x-15$ then, find the value of ${\left(\alpha \beta \right)}^{-1}+{\left(\beta \gamma \right)}^{-1}+{\left(\gamma \alpha \right)}^{-1}$.

If sum of two zeroes of $x^3-a{x}^2+bx-c$ is zero, then prove that $ab=c$.