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