find the value of polynomial 2x+4×-7
Answers
Answer:
Step-by-step explanation:
The other zeroes of the given polynomial are -5 and 3/2
Step-by-step explanation:
Since , two zeroes are √2 and -√2 .
Therefore, (x-√2)(x+√2)=x²-(√2 )²
= x²-2 is a factor of the given polynomial.
Now , we apply the division algorithm to the given polynomial and x²-2.
quotient:2x²+7x-15_______
x²-2)2x⁴+7x³-19x²-14x+30(
*****2x⁴+0-4x²
______________________
********7x³-15x²-14x
********7x³+ 0 -14x
_____________________
***********-15x²+30
********** -15x²+30
_______________________
Remainder ( 0 )
So,
2x⁴+7x³-19x²-14x+30 =(x²-2)(2x²+7x-15)
Now,
2x²+7x-15
Splitting the middle term, we get
= 2x²+10x-3x-15
= 2x(x+5)-3(x+5)
= (x+5)(2x-3)
So, it's zeroes are x=-5 and x =3/2
Therefore,
The other zeroes of the given polynomial are -5 and 3/2
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