if one of the zeroes of the cubic polynomial x3 -7x +6 is 2 ,then the product of the other zeroes is
Answers
the zeroes of the cubic polynomial x3 – 6x2 + 3x + 10 are of the form a,a + b and a + 2b for some real numbers a and b, find the values of a and b as well as the zeroes of the given polynomial.
Given: One of the zeroes of the cubic polynomial x³ -7x + 6 is 2 ,
To Find : The product of the other zeroes
Solution:
cubic polynomial x³ -7x + 6
Sum of zeroes = -0/1 = 0
Sum of product of 2 zeroes taken together = -7/1 = -7
Product of 3 zeroes = -6/1 = -6
One zero is 2
Hence product of other two zeroes = -6/2 = - 3
product of other two zeroes = - 3
Another method :
x²+2x - 3
x- 2 _) x³ -7x + 6 (_
x³ - 2x²
________
2x² -7x + 6
2x² -4x
__________
-3x + 6
-3x + 6
________
0
x²+2x - 3 = (x +3)(x - 1)
Hence other two zeroes are -3 and 1
Product = -3 * 1 = - 3
product of other two zeroes = - 3
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