If sqrt(4x^(4) + 12x^(3) + 25x^(2) + 24x...

If `sqrt(4x^(4) + 12x^(3) + 25x^(2) + 24x + 16) = ax^(2) + bx + c`, then which of the following is true ?

`2b = a - c`

`2a = b +c`

`2b = a + c`

`2b = c -a`

Text Solution

Verified by Experts

The correct Answer is:

(i) Find the square root and equate it to `ax^(2) + bx + c`
(ii) Square on both sides and obtain the value of a, b and c
(iii) Verify the relation between a, b and c

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Consider that f(x) =ax^(2) + bx +c, D = b^(2)-4ac , then which of the following is not true ?

If `a gt 0` then minimum value of f(x) is `(-D)/(4a)`

If `a lt 0`, then maximum value of f(x) is `(-D)/(4a)`

if `a gt 0,D lt 0`, then `f(x) gt 0` for all x ` in ` R

If `a gt 0, D gt 0` , then `f(x) gt 0` for alll ` x in R`

If (x-2) is a factor of x^(4) + ax^(3) - bx^(2) + 18 , then which of the following is correct?

`2a + b + 17=0`

`4a - 2b + 17 =0`.

`2a + b + (17)/(2) =0`

`2a - b - (17)/(2) =0`

If (x+1)and(x-1) are the factors of ax^(3)+bx^(2)+cx+d , then which of the following is true?

`a+b=0`

`b+c=0`

`b+d=0`

`a+c=0`