If (x)=|[x^2+4x-3 2x+4 13] [2x^2+5x-9 4x...

If `(x)=|[x^2+4x-3 2x+4 13] [2x^2+5x-9 4x+5 26] [ 8x^2-6x+1 16 x-6 104]|=a x^3+b x^2+c x+d ,` then `a=3` b. `b=0` c.`c=0` d. none of these

A

`a=3`

B

`b=0`

C

`c=0`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:

B, C

`Delta '(x) = |{:(2x+4,,2x+4,,13),(4x+5,,4x+5,,26),(16x+-6,,16x-6,,104):}|+|{:(x^(2)+4x-3,,2,,13),(2x^(2)+5x-9,,4,,26),(8x^(2)-6x+1,,16,,104):}|`
` =0 +2xx13 xx(0) =0`
`rArr Delta (x) = " constant " rArr a=0,b=0.c=0`

Topper's Solved these Questions

DETERMINANT
CENGAGE PUBLICATION|Exercise Multiple Correct Answer|5 Videos
DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS
CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

If f(x) = |{:(x^2-5x+3,2x-5,3),(3x^2+x+4,6x+1,9),(7x^2-6x+9,14x-6,21):}|=ax^3+bx^2+cx+d then

Solve for x |x-2 2x-3 3x-4 x-4 2x-9 3x-16 x-8 2x-27 3x-64|=0

If x^2+p x+1 is a factor of the expression a x^3+b x+c , then a^2-c^2=a b b. a^2+c^2=-a b c. a^2-c^2=-a b d. none of these

Solve:- (6x^2a^3 - 4x^3a^2 + 8x^4x^2) + 2a^2x^2

Solve : [[x-2,2x-3,3x-4],[x-4,2x-9,3x-16],[x-8,2x-27,3x-64]] =0

Let f(x)=ax^2-bx+c^2, b != 0 and f(x) != 0 for all x ∈ R . Then (a) a+c^2 2b (c) a-3b+c^2 < 0 (d) none of these

If |[x,3, 6],[ 3, 6,x],[6,x,3]|=|[2,x,7],[x,7, 2],[ 7, 2,x]|=|[4, 5,x],[5,x,4],[x,4, 5]|=0, then x is equal to a. 0 b. -9 c. 3 d. none of these

If x satisfies |x-1|+x-2|+|x-3| >= 6, then (a) 0 le x le 4 (b) x le 4 (c) x le 0 or x >= 4 (d) none of these

The combined equation of the asymptotes of the hyperbola 2x^2+5x y+2y^2+4x+5y=0 is (a) 2x^2+5x y+2y^2+4x+5y+2=0 (b) 2x^2+5x y+2y^2+4x+5y-2=0 (c) 2x^2+5x y+2y^2=0 (d) none of these

Solve: |[x^2-1, x^2+2x+1, 2x^2+3x+1], [2x^2+x-1, 2x^2+5x-3, 2x^2+4x-3], [6x^2-x-2, 6x^2-7x+2, 12x^2-5x-2]|=0.

CENGAGE PUBLICATION-DETERMINANTS-All Questions

If (x)=|[x^2+4x-3 2x+4 13] [2x^2+5x-9 4x+5 26] [ 8x^2-6x+1 16 x-6 104]...
Text Solution
|
If P = {1,2}, form set set P xx P xx P
Text Solution
|
Statement 1: If b c+q r=c a+r p=a b+p q=-1, then |{:(ap ,a, p) ,(bq,...
Text Solution
|
If f(theta)=|sinthetacosthetasinthetacosthetasinthetacosthetacosthetas...
Text Solution
|
If f(theta)=|[sin^2A,cot A,1],[sin^2B,cotB,1],[sin^2C,cotC,1]| , then ...
Text Solution
|
The roots of the equation |^x Cr^(n-1)Cr^(n-1)C(r-1)^(x+1)Cr^n Cr^n C(...
Text Solution
|
Let Delta(x)=|[3,3x,3x^2+2a^2] , [3x, 3x^2+2a^2, 3x^3+6a^2x] , [3x^2+2...
Text Solution
|
The determinant |(a^(2)+10,ab, ac),(ab, b^(2)+10, bc),(ac, bc, c^(2)...
Text Solution
|
If f(x)=|[a,-1, 0],[a x, a,-1],[a x^2,a x, a]|,using properties of det...
Text Solution
|
If (x)=|[x^2+4x-3 2x+4 13] [2x^2+5x-9 4x+5 26] [ 8x^2-6x+1 16 x-6 10...
Text Solution
|
If |y z-x^2z x-y^2x y-z^2x z-y^2x y-z^2y z-x^2x y-z^2y z-x^2z x-y^2|=|...
Text Solution
|
Let f(n)=|n n+1 n+2 ^n Pn^(n+1)P(n+1)^n Pn^n Cn^(n+1)C(n+1)^(n+2)C(n+2...
Text Solution
|
If |[ x^n ,x^(n+2) ,x^(2n)],[1 ,x^a , a ],[x^(n+5),x^(a+6),x^(2n+5)]...
Text Solution
|
Let x<1, then value of |[x^2+2, 2x+1 ,1],[ 2x+1,x+2, 1],[ 3, 3 ,1]| is...
Text Solution
|
Find the number of real root of the equation |[0,x-a, x-b],[ x+a,0,x-...
Text Solution
|
Value of |[x+y, z,z ],[x, y+z, x],[y, y, z+x]|, where x ,y ,z are nonz...
Text Solution
|
If e^(itheta)=costheta+isintheta, find the value of |[1,e^(ipi//3),e...
Text Solution
|
Which of the following is not the root of the equation |[x,-6,-1],[ 2,...
Text Solution
|
If A,B,C are the angles of a non right angled triangle ABC. Then find ...
Text Solution
|
Let f(x)=a(5)x^(5)+a(4)x^(4)+a(3)x^(3)+a(2)x^(2)+a(1)x, "where" a(i),s...
Text Solution
|
Evaluate |(cosalphacosbeta,cosalpha sinbeta , - sin alpha),(-sin beta,...
Text Solution
|