If α and β are zeros of polynomial p(x) = x2 – 5x + 6,
then find the value of α + B – 3aß.
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If α and β are zeros of polynomial p(x) = x2 – 5x + 6,
then find the value of α + B – 3aß.
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Answer:
considering alpha=@
and beta=ß
p(x) = x²-5x+6
To find = @+ß+3@ß
we know that :-
@+ß=(-b/a)
=@+ß=-(-5/1) or 5
we know that :-
@ß=(c/a)
=@ß=(6/1) or 6
Putting values of @+ß and @ß in @+ß-3@ß
=(5) - 3(6)
=5-18
=-13
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Answer:
α + β - 3αβ = -13.
Step-by-step explanation:
Given : zeroes of p(x) = x² - 5x + 6 is α and β
Here, a (coefficient of x²) = 1
b (coefficient of x) = - 5
c (constant term) = 6
Sum of zeroes of the polynomial = - (coefficient of x) / (coefficient of x²)
α + β = - b/a
α + β = - (- 5) /1
α + β = 5 —————— (i)
Product of zeroes of the polynomial = (constant term) / (coefficient of x²)
αβ = c/a
αβ = 6/1
αβ = 6 ———————(ii)
α + β - 3αβ = 5 - 3(6) —————— putting values from (i) and (ii)
α + β - 3αβ = 5 - 18
∴ α + β - 3αβ = -13