Question

Given that the zeroes of the cubic polynomial x3 – 6x2 + 3x + 10 are of the form a,a + b, a + 2b for some real numbers a and b, find the values of a and b as well asthe zeroes of the given polynomial.​

Answer 1

Answer:

a=-1,b= 3

Step-by-step explanation:

given equn is

x³-6x²+3x+10

given data that the roots are in AP

so by using elegant rule

let us assume the roots are

p-q ,p ,p+q

now

use the relationship between roots and coefficients

so

S1 = α+β +γ = -B/A

=> p-q+p+p+q=6

3p=6

p=2 ............ important one

then after

S3= αβγ= -D/A

=> p(p+q)(p-q)= -10

=> p(p²-q²)=-10

=> 2(4-q²) = -10

(4-q²) = -5

q² = 9

q=±3

now

you can choose any one value for 'q' as it gives same ans

so

p-q = -1 = a ..........[ as per given condition]

p= 2 = a+b

p+q = 5 = a+2b

so

put value of 'a' in any one given condition

so

and solve it

a+b= 2

b= 2 +1

b = 3

therefore

the roots of cubic polynomial is

-1,2,5

and the values of a and b are

-1 ,3