if α and β are the zeroes of the polynomials x²-px+q then find the values of each of the following.
i)α\β+β\α
ii)αβ³+βα³
iii)α³β² + α²β³
Answers
Answered by
60
If a and b are zeroes of x^2 - px + q, then using the relation between zeroes and coefficients, we get that
Sum of zeroes = a + b = - (-p) = p
Product of zeroes = ab = q
Square on both sides of a + b, we get
a² + b² + 2ab = p² → a² + b² + 2q = p²
a² + b² = p² - 2q
(i) a/b + b/a = (a² + b²)/ab
= (p² - 2q)/q
(ii) ab³ + ba³ = ab(b² + a²)
= q(p² - 2q)
(iii) a³b² + a²b³ = a²b²(a + b)
= (ab)²(a + b)
= q²p
= pq²
Answered by
72
Given that , The α and β are the zeroes of the polynomials x²- px + q .
Exigency To Find : The value of :
- α\β + β\α
- αβ³+βα³
- α³β² + α²β³
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As , We know that ,
⠀⠀⠀⠀⠀AND ,
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As , We know that ,
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As , We know that ,
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