Home
Class 12
MATHS
The total number of distinct x in R for ...

The total number of distinct `x in R` for which `|[x, x^2, 1+x^3] , [2x,4x^2,1+8x^3] , [3x, 9x^2,1+27x^3]|=10` is (A) 0 (B) 1 (C) 2 (D) 3

Text Solution

Verified by Experts

The correct Answer is:
2
` |{:(x,,x^(2),,1+x^(3)),(2x,,4x^(2),,1+8x^(3)),(3x,,9x^(2),,1+27x^(3)):}|=10`
`rArr x^(3) |{:(1,,1,,1+x^(3)),(2,,4,,1+8x^(3)),(3,,9,,1+27x^(3)):}|=10`
`rArr x^(3) |{:(1,,1,,1),(2,,4,,1),(3,,9,,1):}|+x^(6) |{:(1,,1,,1),(2,,4,,8),(3,,9,,27):}|=10`
`rArr x^(3) |{:(1,,0,,0),(2,,2,,-1),(3,,6,,-2):}|+x^(6) |{:(1,,0,,0),(2,,2,,6),(3,,6,,24):}|=10`
`rArr 6x^(6) +x^(3)-5=0`
`rArr (6x^(3) -5) (x^(3) +1) =0`
`rArr x^(3) =5//6 " or " x^(3) =-1`
Two real distinct values of x
Promotional Banner

Similar Questions

Explore conceptually related problems

The , total number of distinct x in R for which det[[x,x^(2),1+x^(3)2x,4x^(2),1+8x^(3)3x,9x^(2),1+27x^(3)]]=10 is (A)0(B)1(C)2 (D) 3,

Total number of positive integers x for which f(x)=x^(3)-8x^(2)+20x-13 is prime number,is 1 b.2 c.3 d.4

The number of pairs (a,b) for which a(x+1)^(2)+b(x^(2)-3x-2)+x+1=0AA x in R

Total number of positive integers x for which f(x)=x^(3)-8x^(2)+20x-13 is a prime number,is 1( b) 2(c)3 (d) 4

The number of pairs (a,b) for which a(x+1)^2+b(x^(2)-3x-2)+x+1=0 AA x in R is :

Which of the following is not the root of the equation |[x,-6,-1],[ 2,-3x,x-3],[-3, 2x,x+2]|=0? a.2 b. 0 c. 1 d. -3

If X^2+4x+3=0 , then the value of (X^3)/(X^6+27x^3+27 is (A) -1 (B) -frac(1)(2) (C) 1 (D) 1/2

If (x_i , 1/x_i), i = 1, 2, 3, 4 are four distinct points on a circle, then (A) x_1 x_2 = x_3 x_4 (B) x_1 x_2 x_3 x_4 = 1 (C) x_1 + x_2 + x_3 + x_4 = 1 (D) 1/x_1 + 1/x_2 + 1/x_3 + 1/x_4 = 1

IF ax^3+bx^2+cx+d = |(x^2,(x-1)^2, (x-2)^2),((x-1)^2 (x-2)^2, (x-3)^2), (x-2)^2, (x-3)^2, (x-4)^2)| , then d= (A) 1 (B) -8 (C) 0 (D) none of these

Number of roots which are common to the equations x^(3)+2x^(2)+2x+1=0 and x^(2008)+x^(2009)+1=0, are (A)0(B)1(C)2 (D) 3