If alpha and beta are the zeroes of the polynomial x²+8x+6 form a ploynomial whose zeroes are alpba-beta and alpha+beta
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Answers
Step-by-step explanation:
Since (Alpha +Beta) and (Alpha-Beta) are two zeros,
Sum of Zeros= A+B +A-B
=2A-----------------1
Product of Zeros= (A+B)(A-B). [use identity:(a+b)(a-b)= a²-b²]
=A²-B²-------------2
Sum of zeros = -b
a
= -8
So Iets assume its = 2× (-4)------------Substituted the value of alpha (A)
= -8
Product of zeros= c
a
=6
So I assume it is= A²-B²
=(-4)²-(√10)²
=16-10
=6
So I am verifying,
Formula for required quad.poly.=x ²-(sum of zeros)x+ (product of zeros)
= x² -(2A )x+(A²-B²)
=x²-2×(-4)x + (-4)²-(√10)²
=x²+8x+6
So the zeros are 4+√10 and 4-√10
Or the value of Alpha is 4 and Beta is √10.
I can understand it is hard to analyze but since you didn't gave any options, I have given two answers. Hope you understood it well.
And whoever is reading please tell if you understood.☺
Note(Important):Zeros like (4+√10) , (7+√4) , (3+√2)...always exist in pairs like (a+b) and (a-b).