Question

If alpha and beta are the zeros of the polynomial x square - 2 x minus 15 then the find the polynomial those zeros are 2Alpha and 2Bets

Answer 1

Answer:

$p(x) = {x}^{2} - 2x - 15 \\ = {x }^{2} - 5x + 3x - 15 \\ = x(x - 5) + 3(x - 5) \\ =( x - 5)(x + 3) \\ = \alpha = 5 \: and \: \beta = - 3 \\ 2 \alpha = 10 \: and \: 2 \beta = - 6$

sum of zeroes =-b/a

(10)+(-6)=-b/a

4=-b/a

b=-4

product of zeroes =c/a

(10)(-6)=c/a

-60=c/a

c =-60

the equation is

$a {x}^{2} + bx + c \\ = {x}^{2} - 4x - 60$