Question

If alfa _ beta, alfa and alfa + beta are the zeroes of the polynomial of (x)=x cube _ 12xsquare +39x + k then find the value of k​

Answer 1

Let α= a-d

β =a

γ=a+d

So,

α+β+γ=12

=》(a-d)+(a)+(a+d)=12

=》3a=12

=》a=4

αβ+βγ+αγ=39

(a-d)a+(a+d)a+(a-d)(a+d)=39

Note:-

Please solve it, then you will get-

d=+3 or -3

Hence,

1》α=a-d

or,

4-

=1

or,

4-(-3)

=7

2》β=4

3》γ=》4+3=7

or,

4+(-3)

=1

Hence,

αβγ= -k

.•.-k=1 × 4 × 7

So,

k = -28