Question

The zeroes of the polynomial x -3x - m(m - 3) = 2 are.​

Answer 1

Answer:

${x}^{2} - 3x - m(m - 3) = 2$

${x}^{2} - 3x - m(m - 3) - 2 = 0$

The roots,

$\alpha + \beta = 3$

And

$\alpha \beta = - (m(m - 3) + 2)$

$\alpha = 3 - \beta$

Put in the product

$\beta (3 - \beta ) = - (m(m - 3) + 2)$

${ \beta }^{2} - 3 \beta - (m(m - 3) + 2) = 0$

$\beta = \frac{3 + \sqrt{(m(m - 3) + 2)}}{2}$

$\alpha = 3 - \frac{3 + \sqrt{(m(m - 3) + 2)}}{2}$

$\alpha = \frac{3 + \sqrt{(m(m - 3) + 2)}}{2}$