Question

if alpha beta gama are zeroes of acubic polynomial x3 - 12x2+44x+c and 2alpha=beta +gama that find value of c​

Answer 1

Step-by-step explanation:

we know α+β+Φ=-b/a------------------(1)

so from equation 12/1

we know 2α=β+Φ

so α=β+Φ/2

subs the value of alpha in (1)

β/2+Φ/2+β+Φ=12

so β+Φ=8

we know 2α=β+Φ

here 2α=8

α=4

we know α.β.Φ=-d/a

4βΦ=c

so βΦ=c/4

β=c/4Φ

taking 2 at a time

αβ+ βΦ+Φα=44

4β+c+4Φ=44

4(β+Φ)=44-c----β+Φ=44-c/4(took β+Φ)

c+4Φ/4=8( 2α=β+Φ)

8=44-c/4(α=4)

32=44-c

so C=12