M L Aggarwal Solutions for Chapter: Polynomials, Exercise 3: Exercise 2.3

If the sum of zeroes of the polynomial $(a+1)x^2+(2a+3)x+(3a+4)$ is $-1,$ then the product of zeroes is _____?

If one zero of the polynomial $3x^2-8x+2k+1$ is seven times the other, then the value of $k$ is _____?

Find all the zeroes of the polynomial $x^3+3x^2-2x-6$ if two of its zeroes are $\sqrt{2}$ and $-\sqrt{2}$.

Find a quadratic polynomial with the given numbers as the sum and product of its zeroes:

$4,3$

Find a quadratic polynomial with the given numbers as the sum and product of its zeroes:

$-3,2$

Find a quadratic polynomial with the given numbers as the sum and product of its zeroes:

$0,-\sqrt{2}$

Find a quadratic polynomial whose product and sum of zeroes are $\frac{-13}{5}$ and $\frac{-3}{5}$ respectively.

Find a quadratic polynomial whose product and sum of zeroes are $\frac{-1}{3}$ and $\frac{-7}{2}$ respectively.