Obtain all other zeros of a polynomial 2 x ki power 4 + 3 x cube - 15 x square minus 24 x minus 8 if two of its zeros are 2 root 2 and minus 2 root 2
Answers
Answer:
Step-by-step explanation:
Solve the equation x3 − 3x2 – 2x + 4 = 0
We put the numbers that are factors of 4 into the equation to see if any of them are correct.
f(1) = 13 − 3×12 – 2×1 + 4 = 0 1 is a solution
f(−1) = (−1)3 − 3×(−1)2 – 2×(−1) + 4 = 2
f(2) = 23 − 3×22 – 2×2 + 4 = −4
f(−2) = (−2)3 − 3×(−2)2 – 2×(−2) + 4 = −12
f(4) = 43 − 3×42 – 2×4 + 4 = 12
f(−4) = (−4)3 − 3×(−4)2 – 2×(−4) + 4 = −100
The only integer solution is x = 1. When we have found one solution we don’t really need to test any other numbers because we can now solve the equation by dividing by (x − 1) and trying to solve the quadratic we get from the division.
the other zeroes are -1/2 and -1
Step-by-step explanation:
given polynomial : 2x⁴+3x³-5x²-9x-3
2 of its zeroes are +√3 and -√3
let the zeroes be (x+√3)(x-√3)
hence zeroes = x²-(√3)²
=x²-3
now dividing polynomial by x²-3..
x²-3) 2x⁴+3x³-5x²-9x-3 ( 2x²+3x+1
2x⁴ -6x²
⁽⁻⁾ ⁽⁺⁾
⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻
3x³+ x²-9x
3x -9x
⁽⁻⁾ ⁽⁺⁾
⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻
x²-3
x²-3
⁽⁻⁾ ⁽⁺⁾
⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻
0 0
now factorising, 2x²+3x+1
2x²+2x+1x+1
2x(x+1)+1(x+1)
(2x+1)(x+1)=0
2x+1=0 x+1=0
2x= -1 x= -1
x = -1/2
therefore all zeroes are -1/2 and -1, 2√2, -2√2