1} Find all the zeroes of 2x4-3x3-3x2+6x-2 two of its zeroes are √2, √-2.
2} Find the zeroes and verify that relationship between and coefficient:
i) 4x2-4x+1 ii) 6x2-7x-3
3} Solve for x and y: x+6/y=6 , 3x-8/y=5
4} x+1/2 + y-1/3=8 , x-2/3 + y+1/2=9
5}Solve for x and x/a and x/a+y/b=2 :
ax-by=a2-b2
THE CORRECT ONES WILL BE MARKED AS BRAINLIST
Answers
Answer:
HELLO DEAR,
x/a + y/b = 2
ay + xb = 2ab----------( 1 )
ax - by = a² - b²---------( 2 )
from-----( 1 ) &-------( 2 )
multiply ( 1 ) by "a" ( 2 ) by "b"
abx + a²y = 2a²b
abx - b²y = ba² - b³
-------------------------------------------------
y(a² + b²) = 2a²b - ba² + b³
y(a² + b²) = a²b + b³
y(a² + b²) = b(a² + b²)
y = b [ put in -----( 1 )]
we get,
ay + xb = 2ab
a(b) + xb = 2ab
xb = 2ab - ab
x = ab/b
x = a
3)x+6/y=6 and 3x-8/y=5
x+6=6y and 3x-8=5y
x-6y=-6--- x 3
3x-5y=8----x 1
3x-18y=-18
3x-5y=8
-13y=-26
y=2
x=6
Step-by-step explanation:
2)4s2 – 4s + 1
We have p(s) = 4s2 – 4s + 1
= 4s2 – 2s – 2s + 1 = 2S (2S – 1) –1 (2s – 1)
= (2s – 1) (2s – 1)
For p(s) = 0, we have,
see attachment 1 and then 2
Thus, the relationship between the zeroes and coefficients in the polynomial 4s2 – 4s + 1 is verified.
2)(iii) 6x2 – 3 – 7x
We have
p (x) = 6x2 – 3 – 7x
= 6x2 – 7x – 3
= 6x2 – 9x + 2x – 3
= 3x (2x – 3) + 1 (2x – 3)
= (3x + 1) (2x – 3)
For p (x) = 0, we have,
see attachment 3
hope it helps................
