If a and b are zeroes of px =3x^2-5x-2 then evaluate a^3 + b^2
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the answer is 23/108
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p(x) = 3x² - 5x - 2 = 0
3x² - 6x + x - 2 = 0
3x(x - 2) + 1(x-2) = 0
(x - 2) (3x + 1) = 0
→ x-2 = 0 ; x = 2
→ 3x + 1 = 0 ; x = -1/3
a and b are zeroes of the polynomial.
Therefore, a = 2 and b = -1/3
→ a³ + b² = 2³ + (-1/3)²
= 8 + 1/9
= (72+1)/9
= 73/9
If a = -1/3 and b = 2 then
→ a³ + b² = (-1/3)³ + 2²
= -1/27 + 4
= (-1+108)/27
= 107/27
3x² - 6x + x - 2 = 0
3x(x - 2) + 1(x-2) = 0
(x - 2) (3x + 1) = 0
→ x-2 = 0 ; x = 2
→ 3x + 1 = 0 ; x = -1/3
a and b are zeroes of the polynomial.
Therefore, a = 2 and b = -1/3
→ a³ + b² = 2³ + (-1/3)²
= 8 + 1/9
= (72+1)/9
= 73/9
If a = -1/3 and b = 2 then
→ a³ + b² = (-1/3)³ + 2²
= -1/27 + 4
= (-1+108)/27
= 107/27
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