Find all the zeroes of x³+11x²+23x-35 if two of its zeroes are 1 and -5
Answers
Answer:
The zeroes of x³+11x²+23x-35 are 1, -5, and -7.
Step-by-step explanation:
Find all the zeroes of x³+11x²+23x-35 if two of its zeroes are 1 and -5
Use one of the zeroes of x³+11x²+23x-35 which is 1 applying Synthetic Division Method to find the other zeroes.
1 ] 1 11 23 -35 Write the numerical coefficients of x³+11x²+23x-35
1 12 35 Bring down, multiply by 1, add the product to 11, multiply again
1 12 35 0 Use these numbers as numerical coefficients of new equation
1x² + 12x + 35 = 0
x² + 12x + 35 = 0 Apply factoring.
(x + 7) (x + 5) = 0
x + 7 = 0 x + 5 = 0 Solve for each value of x.
x + 7 +(-7) = 0 +(-7) x + 5 +(-5) = 0 +(-5) Apply APE.
x + 0 = 0 - 7 x + 0 = 0 - 5 Simplify.
x = -7 x = -5
Use another zero of x³+11x²+23x-35 which is -5 applying Synthetic Division Method to find the other zeroes.
-5 ] 1 11 23 -35 Write the numerical coefficients of x³+11x²+23x-35
-5 -30 35 Bring down, multiply by -5, add the product to 11, ...
1 6 -7 0 Use these numbers as numerical coefficients of new equation
1x² + 6x - 7 = 0
x² + 6x - 7 = 0 Apply factoring.
(x + 7) (x - 1) = 0
x + 7 = 0 x - 1 = 0 Solve for each value of x.
x + 7 +(-7) = 0 +(-7) x - 1 + 1 = 0 + 1 Apply APE.
x + 0 = 0 - 7 x + 0 = 0 + 1 Simplify.
x = -7 x = 1
Answer:
The zeros are 1, -5 , -7
Step-by-step explanation:
Let P(x) = x³+11x²+23x-35
Given: zeros of P(x) are 1 and -5
sum of the zeros = -4
product of the zeros =-5
corresponding factor is
x² - (sum of the zeros)x+(product of the zeros)
x² -(-4)x-5
x² + 4x-5
we have to find the remaining one zero
Now, the given polynomial can be written as
x³+11x²+23x-35 =(x² + 4x-5)(x+7)
Then clearly the remaining one zero is -7
Note:
Easy way to find the factor (x+7)
dividing x³ by x² we get x
dividing -35 by -5 we get -7