3.
The roots of the equation x?+6x-4= 0 are a., B.
Find the quadratic equation whose roots are
2 2
(i) a? and B
and
(iii) a?B and B²C .
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Answer:
p(x) = x² + 6x - 4 = 0
Find the quadratic equation whose roots are α2 and β2
★ Given polynomial = x² + 6x - 4 = 0
a = 1
b = 6
c = -4
α + β = -b/a
⠀⠀⠀⠀⠀➝α + β = -6/1
⠀⠀⠀⠀⠀➝α + β = -6
αβ = c/a
⠀⠀⠀⠀⠀➝ -4/1
⠀⠀⠀⠀⠀➝ -4
α² + β² = (α + β)² - 2αβ
⠀⠀⠀⠀⠀➝ α² + β² = (-6)² - 2× -4
⠀⠀⠀⠀⠀➝ α² + β² = 36 + 8
⠀⠀⠀⠀⠀➝ α² + β² = 44
The quadratic polynomial whose roots are α² and β²
★ Formula for quadratic equation :-
x² - (α + β)x + αβ
⠀⠀⠀⠀⠀➝ x² - (α² + β²)x + α²β²
⠀⠀⠀⠀⠀➝ x² - (44)x + (-4)²
⠀⠀⠀⠀⠀➝ x² - 44x + 16
So,
the quadratic equation whose roots are α2 and β2 is ★ x² - 44x + 16.
Step-by-step explanation:
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