if alpha and beta are zeroes of polynomial such that alpha+beta =6 and alpha*beta =4 then write the polynomial find alpha and beta
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Answered by
2
the answer is x^2-6x+4
RadhaRamam:
please make my answer as brainliest
also find alpha and beta
3+√20,3-√20
its wrong....
i got it its write......
then please mark my answer as brainliest
ok
Answered by
7
alpha + beta = -b/a
= 6
= -(-6)/1
alpha × beta = c/a
= 4
= 4/1
So,
a = 1
b = -6
c = 4
Now,
ax² + bx + c =0
Substituting the values,
x² -6x + 4 = 0
Now, finding the discriminant,
b² - 4ac = (-6)² - 4×1×4
= 36 - 16
= 20
So the given equation has two distinct roots.
Quadratic formula,
x = (-b ± √ b² - 4ac)/2a
= ( -(-6) ± √ 20 )/2
= ( 6 ± 2√5) / 2
= 3 ±√5
Case I,
x = 3 + √5
Case II,
x = 3 - √5
= 6
= -(-6)/1
alpha × beta = c/a
= 4
= 4/1
So,
a = 1
b = -6
c = 4
Now,
ax² + bx + c =0
Substituting the values,
x² -6x + 4 = 0
Now, finding the discriminant,
b² - 4ac = (-6)² - 4×1×4
= 36 - 16
= 20
So the given equation has two distinct roots.
Quadratic formula,
x = (-b ± √ b² - 4ac)/2a
= ( -(-6) ± √ 20 )/2
= ( 6 ± 2√5) / 2
= 3 ±√5
Case I,
x = 3 + √5
Case II,
x = 3 - √5
Thank you
u r Also a generous in maths
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