Question

y = 2x^2 + ax + 14.

a is a constant.

it can also be written as y = 2(x - 3)^2 + b

b is also a constant :P

help me find the values of a and b. i'll give the next part once you find the first.

Answer 1

1 minute

Answer 2

ax-b+8=0

Answer 3

how??

Answer 4

Given, y= 2x^2 + ax + 14, also y= 2(x-3)(x-3) + b

Answer 5

So, 2x^2 + ax + 14 = 2(x-3)(x-3) + b

Answer 6

Solve and u will get the above relation.

Answer 7

what have you tried ?

Answer 8

i'm trying to complete the square, for the first eq.

Answer 9

Hm no need just expand the second and compare the coefficients, you will get \( a=-12 \) and \( b=-4 \)

Answer 10

can u explain in detail?
How u got the coefficient?

Answer 11

\[ 2x^2 + ax + 14 = 2(x - 3)^2 + b \Rightarrow 2x^2 + ax + 14 = 18-12 x+2 x^2 +b \]

Now compare the coefficients of both sides, to get the result.

Answer 12

Is this extended maths?

Answer 13

Plzz say the last step

Answer 14

ohhhhhh, smart. I never thought of that :P nopeee, this is add maths.

Answer 15

Now, ax + 14= b+18-12x

Answer 16

\[ 2x^2 + ax + 14 = 2 x^2 -12 x+ 18 +b \] Now ?

Answer 17

then?

Answer 18

Think adarsh it's not much difficult after this..

Answer 19

and add maths is advance maths?

Answer 20

see, i got like this:

ax - b= -12x + 4

Answer 21

yes so, that means a=12 and b=-4.

Answer 22

Ohhhhhhhhhhhhhh, I understand. THanksssssssssss.

Answer 23

Glad to help.

Answer 24

Thanbks a lot, FOOLForMaths. And Thyanks Tanvi, for bringing such a challenging question.

Answer 25

y = 2x^2 + ax + 14
y = 2(x - 3)^2 + b

\[=> 2x^2 + ax + 14 = 2(x^2-6x+9)+b\]
\[=>2x^2 + ax + 14 = 2x^2-12x+(18+b)\]

equating on both sides,
we get \[a = -12x; 14=18+b\]
so, a = -6 and b = -4

Answer 26

^^ a=-6 ?!