Question

If α and β are zeroes of polynomialx2 - 2x +3 then form quadratic polynomial with zeroes
a) α+ 2 and β +2
b ) α- 1 / α+ 1 and β -1 / β + 1

Relevant answers please​

Answer 1

Answer:

$x }^{2} - 2x - 3$

$x {}^{2} - (3 - 1)x - 3$

$x {}^{2} - 3x + x - 3$

$x(x - 3) + 1(x - 3)$

$(x - 3)(x + 1)$

$\alpha = 3 \: \: \beta = - 1$

a)

$\alpha + 2 = 3 + 2 = 5$

$\beta + 2 = - 1 + 2 = 1$

b)

$\frac{ \alpha - 1}{ \alpha + 1} = \frac{3 - 1}{3 + 1} = \frac{2}{4} = \frac{1}{2}$

$\frac{ \beta - 1}{ \beta + 1} = \frac{ - 1 - 1}{ - 1 + 1 } = \frac{ - 2}{0}$