Question

If a and ß are the zeroes of a polynomial x2-x-30, then form a quadratic Polynomial whose zeroes are 2-a and 2- B​

Answer 1

Answer:

X2 - 3x -28

Step-by-step explanation:

Answer 2

x² - x - 30

= x² - 6x + 5x - 30

= x(x - 6) + 5(x - 6)

= (x + 5)(x - 6)

to find zeroes,

(x + 5)(x - 6) = 0

x = -5 or x = 6

hence, let $\alpha = -5 \: and \: \beta = 6$

$now, \: 2 - \alpha = 2 - (-5) = 2 + 5 = 7 \\</p><p>and \: 2 - \beta = 2 - 6 = -4$

hence, polynomial with $2 - \alpha \: and \: 2 - \beta$ as zeroes is–

p(x) = x² - (sum of roots)x + (product of roots)

p(x) = x² - [7 + (-4)]x + (7)(-4)

p(x) = x² - 3x - 28