Question

If α and β are the zeroes of the quadratic polynomial 3x2 – 2x – 6 then find the value of α2 + β2​

Answer 1

Answer:

for a polynomial ax²+ bx +c,

sum of zeroes = -b/a

product of zeroes = c/a

Similarly for p(x)= 3x²+2x-6

a+b = -2/3

ab = -6/3 = -2

1. a-b:

(a-b)² = (a+b)²-4ab

= (-2/3)² -4(-2)

= 4/9 +8

= (4+9×8)/9

= 76/9

a-b = √76/3

2. a²+b² = (a+b)² -2ab

= (-2/3)² -2(-2)

= 4/9 +4

= 40/9

3. a³+b³ = (a+b)³ -3ab(a+b)

= (-2/3)³ -3(-2)(-2/3)

= -8/27 - 4

= -116/27

4. 1/a + 1/ b

= (a+b)/ab

= (-2/3)/(-2)

= 1/3

I hope you understand the approach.

Just play with the identities.

All the best!

And please check the calculations also.

Step-by-step explanation: