Question

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If α and β are the zeroes of the quadratic polynomials given below
p(x) = 4x2 – 5x – 1
p(x) = 6x2 + x – 2
p(x) = x2 – 4x + 3
Then evaluate:
α^2+ β^2
α/β + β/α
α^3+ β^3
1/α^3 +1/β^3
α^2 β + αβ^2

Answer 1

Answer:

Hey!

Given polynomial :- 4x²-5x-1

and alpha beta are it's zeros !

• Sum of Zeros =

= \frac{ - coefficient \: of \: x}{coefficient \: of \: {x}^{2} }=

coefficientofx

2

−coefficientofx

\alpha + \beta = \frac{5}{4}α+β=

4

5

• Product of Zeros =

\frac{constant \: term}{coeff. \: \: of \: {x}^{2} }

coeff.ofx

2

constantterm

\alpha \beta = \frac{ - 1}{4}αβ=

4

−1

# To find

{ \alpha }^{2} \beta + \alpha { \beta }^{2}α

2

β+αβ

2

\alpha \beta ( \alpha + \beta )αβ(α+β)

\frac{ - 1}{4} \times \frac{5}{4} = \frac{ - 5}{16}

4

−1

×

4

5

=

16

−5

Hence , value is -5/16

Step-by-step explanation:

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