Question

alpha, beta, gamma are the zeros of the cubic polynomial x cube minus 12 x square + 44 X + c if 2 b is equal to Alpha+ gamma, find the value of c ​

Answer 1

$\huge\boxed {Answer}$

Given :-

Alpha , beta and gama are the zeroes of

the cubic polynomial -

x³ - 12x² + 44x + c

Also given , Alpha + gama = 2beta

Have to Find out :-

Value of c

Solution :-

We know that -

alpha + beta + gama = -b/a

2beta + beta = 12

3beta = 12

beta = 4

then , alpha + gama = 8

we also know that -

Alpha*beta* gama = -d/a

4alpha*gama = -c

alpha*gama = -c/4

Along with it ,

we remember that

alpha beta + beta*gama + gama*

alpha = c/a

beta(alpha + gama) + (-c/4) = 44

4 (8) + (-c/4) = 44

32 - c/4 = 44

-c/4 = 12

-c = 12 × 4

c = -48

Result :-

Value of c = -48