Answer:
- The value of
![a = -20](https://tex.z-dn.net/?f=a%20%3D%20-20)
- The value of
![b=-25](https://tex.z-dn.net/?f=b%3D-25)
Step-by-step explanation:
Let
![p(x)=6x^4+8x^3-5x^2+ax+b](https://tex.z-dn.net/?f=p%28x%29%3D6x%5E4%2B8x%5E3-5x%5E2%2Bax%2Bb)
and
![q(x)=2x^2-5](https://tex.z-dn.net/?f=q%28x%29%3D2x%5E2-5)
As
is exactly divisible, so, the remainder is 0.
∴ ![p(x)=q(x).g(x)+r(x)](https://tex.z-dn.net/?f=p%28x%29%3Dq%28x%29.g%28x%29%2Br%28x%29)
![6x^4 + 8x^3 - 5x^2 + ax + b = (\sqrt{2} x - \sqrt{5})(\sqrt{2} x + \sqrt{5}) g(x)](https://tex.z-dn.net/?f=6x%5E4%20%2B%208x%5E3%20-%205x%5E2%20%2B%20ax%20%2B%20b%20%3D%20%28%5Csqrt%7B2%7D%20x%20-%20%5Csqrt%7B5%7D%29%28%5Csqrt%7B2%7D%20x%20%2B%20%5Csqrt%7B5%7D%29%20g%28x%29)
As the R.H.S becomes 0 when
and
.
And
by substituting ![x = \sqrt{\frac{5}{2} }](https://tex.z-dn.net/?f=x%20%3D%20%5Csqrt%7B%5Cfrac%7B5%7D%7B2%7D%20%7D)
![6(\sqrt{\frac{5}{2} } )^4 + 8(\sqrt{\frac{5}{2} } )^3 - 5(\sqrt{\frac{5}{2} } )^2 + a(\sqrt{\frac{5}{2} } ) + b = 0](https://tex.z-dn.net/?f=6%28%5Csqrt%7B%5Cfrac%7B5%7D%7B2%7D%20%7D%20%29%5E4%20%2B%208%28%5Csqrt%7B%5Cfrac%7B5%7D%7B2%7D%20%7D%20%29%5E3%20-%205%28%5Csqrt%7B%5Cfrac%7B5%7D%7B2%7D%20%7D%20%29%5E2%20%2B%20a%28%5Csqrt%7B%5Cfrac%7B5%7D%7B2%7D%20%7D%20%29%20%2B%20b%20%3D%200)
![25 + 20( \frac{\sqrt{5}}{\sqrt{2}} ) + a( \frac{\sqrt{5}}{\sqrt{2}}) +b =0...[A]](https://tex.z-dn.net/?f=25%20%2B%2020%28%20%5Cfrac%7B%5Csqrt%7B5%7D%7D%7B%5Csqrt%7B2%7D%7D%20%29%20%2B%20a%28%20%5Cfrac%7B%5Csqrt%7B5%7D%7D%7B%5Csqrt%7B2%7D%7D%29%20%2Bb%20%3D0...%5BA%5D)
by substituting ![x = -\sqrt{\frac{5}{2} }](https://tex.z-dn.net/?f=x%20%3D%20-%5Csqrt%7B%5Cfrac%7B5%7D%7B2%7D%20%7D)
![25 - 20( \frac{\sqrt{5}}{\sqrt{2}} ) - a( \frac{\sqrt{5}}{\sqrt{2}}) +b =0.....[B]](https://tex.z-dn.net/?f=25%20-%2020%28%20%5Cfrac%7B%5Csqrt%7B5%7D%7D%7B%5Csqrt%7B2%7D%7D%20%29%20-%20a%28%20%5Cfrac%7B%5Csqrt%7B5%7D%7D%7B%5Csqrt%7B2%7D%7D%29%20%2Bb%20%3D0.....%5BB%5D)
Adding Equation [A] and equation [B]
![50 +2b =0](https://tex.z-dn.net/?f=50%20%2B2b%20%3D0)
![b=-25](https://tex.z-dn.net/?f=b%3D-25)
Subtracting Equation [A] and equation [B]
![40(\sqrt{\frac{5}{2} } ) + 2a(\sqrt{\frac{5}{2} } ) =0](https://tex.z-dn.net/?f=40%28%5Csqrt%7B%5Cfrac%7B5%7D%7B2%7D%20%7D%20%29%20%2B%202a%28%5Csqrt%7B%5Cfrac%7B5%7D%7B2%7D%20%7D%20%29%20%3D0)
![a = -20](https://tex.z-dn.net/?f=a%20%3D%20-20)
Therefore,
- The value of
![a = -20](https://tex.z-dn.net/?f=a%20%3D%20-20)
- The value of
![b=-25](https://tex.z-dn.net/?f=b%3D-25)
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Answer:
1799.08748
Rounded version: 1799
Step-by-step explanation:
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Answer:
4x + (5x+18) = 180-81=99
9x+18=99
9x=99-18=81
x=9
Step-by-step explanation:
Answer:
C(t)=3000(1.002417)^12t+960t
if T=1 year then the saving will be : 4048.17
Step-by-step explanation:
3000 deposit amount, 2.9 compound monthly interest . save 80 dollars per month at home .
A=p(1+r)^t
A=3000(1+0.029/12)^12t
A=3000(1.002417)^12t dollars
for the amount saved at home=80*12t=960t dollars
C(t)=3000(1.002417)^12t+960t
if T=1 year then the saving will be :
C(t)=3000(1.002417)^12t+960t
=3088.17+960= 4048.17 dollars