Vachmi

1
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

(i) $x^2 - 2x -8$
(ii) $4s^2 - 4s + 1$
(iii) $6x^{2}-3-7x$
(iv) $4u^{2}+8u$
(v) $t^{2}-15$
(vi) $3x^{2}-x-4$


Solution
Polynomial long division


Polynomial long division


Polynomial long division


Polynomial long division


Polynomial long division


Polynomial long division



2
Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively:

(i) $\dfrac{1}{4}$, -1
(ii) $\sqrt{2}$, $\dfrac{1}{3}$
(iii) 0, $\sqrt{5}$
(iv) 1, 1
(v) $\dfrac{-1}{4}$, $\dfrac{1}{4}$
(vi) 4, 1


Solution

Polynomial long division


Polynomial long division


Polynomial long division


Polynomial long division
Polynomial long division


Polynomial long division