Karnataka Board Solutions for Chapter: Solved Examples, Exercise 2: Exercise 2

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

Find the zeroes of the polynomial $x^2-3$ and verify the relationship between the zeroes and the coefficients.

Find a quadratic polynomial, the sum and product of whose zeroes are $-3$ and $2$, respectively.

Verify that $3, -1, -\frac{1}{3}$ are the zeroes of the cubic polynomial $p\left(x\right)=3x^3-5x^2-11x-3$, and then verify the relationship between the zeroes and the coefficients.

Divide $2x^2+3x+1$ by $x+2$

Divide $3x^3+x^2+2x+5$ by $1+2x+x^2$.

Divide $3x^2-x^3-3x+5$ by $x-1-x^2$, and verify the division algorithm.

Find all the zeroes of $2x^4-3x^3-3x^2+6x-2$, if you know that two of its zeroes are $\sqrt{2}$ and $-\sqrt{2}$.