|{:(a,b,ax+by),(b,c,bx+cy),(ax+by,bx+cy,...

`|{:(a,b,ax+by),(b,c,bx+cy),(ax+by,bx+cy,0):}|=(b^2-ac)(ax^2+2bxy+cy^2)`

Topper's Solved these Questions

DETERMINANT
CHHAYA PUBLICATION|Exercise EXERCISE 2C|37 Videos
DETERMINANT
CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (Multiple Correct Answers Type)|5 Videos
DETERMINANT
CHHAYA PUBLICATION|Exercise EXERCISE 2A|36 Videos
DEFINITE INTEGRAL AS AN AREA
CHHAYA PUBLICATION|Exercise Assertion-Reason Type|2 Videos
DIFFERENTIAL EQUATIONS OF THE FIRST ORDER AND FIRST DEGREE
CHHAYA PUBLICATION|Exercise E ASSERTION-REASON TYPE|2 Videos

Similar Questions

Explore conceptually related problems

If a >0 and discriminant of a x^2+2b x+c is negative, then |[a,b,ax+b],[b,c,bx+c],[ax+b,bx+c,0]| is a. +v e b. (a c-b)^2(a x^2+2b x+c) c. -v e d. 0

If a gt 0 and discriminant of ax^(2)+2bx+c=0 is negative, then the value of - |(a,b,ax+b),(b, c,bx+c),(ax+b,bx+c,0)| is -

If u=ax+by+cz , v=ay+bz+cx , w=az+bx+cy , then the value of |{:(a,b,c),(b,c,a),(c,a,b):}|xx|{:(x,y,z),(y,z,x),(z,x,y):}| is

IF y^2=ax^2+2bx+c , Prove that (d^2x)/(dy^2)=(b^2-ac)/(ax+b)^3 .

If x,y,z are the perpendiculars from the vertices of a triangle ABC on the opposite sides a,b,c respectively, then show that (bx)/c+(cy)/a+(az)/b=(a^2+b^2+c^2)/(2R)

The roots of the equation ax^2 - bx + c = 0 are .. 1.x =' (-b pm sqrtb^2 - 4ac)/(2a) 2.x =' (b pm sqrtb^2 - 4ac)/(2a)'

Solve: (x^2-ax)/b+(x^2-bx)/a+(x^2-3ax-3bx)/(a+b)=0 ]

(bz+cy)/a=(cx+az)/b=(ay+bx)/c then prove x/(a(b^2+c^2-a^2))=y/(b(c^2+a^2-b^2))=z/(a(a^2+b^2-c^2))

IF alpha and beta be the roots of ax^2+2bx+c=0 and alpha+delta,beta+delta be those of Ax^2+2Bx+C=0 , prove that , (b^2-ac)/a^2=(B^2-AC)/A^2

If x = cy + bz, y = az + cx , z =bx + ay, then prove that x^2/(1-a^2)= y^2/(1-b^2)

CHHAYA PUBLICATION-DETERMINANT -EXERCISE 2B

|{:(" "a^2," "bc,c^2+ca),(a^2+ab," "b^2," "ca),(" "ab,b^2+bc," "c^2...
Text Solution
|
|{:(2costheta,1,0),(1,2costheta,1),(0,1,2costheta):}|=(sin4theta)/(sin...
Text Solution
|
|{:(a,b,ax+by),(b,c,bx+cy),(ax+by,bx+cy,0):}|=(b^2-ac)(ax^2+2bxy+cy^2)
Text Solution
|
|{:(3x^2,3x,1),(x^2+2x,2x+1,1),(2x+1,x+2,1):}|=(x-1)^3
Text Solution
|
|{:(x+y+z," "-z," "-y),(" "-z,x+y+z," "-x),(" "-y," "-x...
Text Solution
|
|{:(1,1,1),(""^(n)c1,""^(n+1)c1,""^(n+2)c1),(""^(n+1)c2,""^(n+2)c2,""^...
Text Solution
|
|{:(x+y+z," "-z," "-y),(" "-z,x+y+z," "-x),(" "-y," "-x...
Text Solution
|
|{:(cos(x+y),sin(x+y),-cos(x+y)),(sin(x-y),cos(x-y),sin(x-y)),(sin2x,0...
Text Solution
|
prove that, |{:(0,cosalpha,-sinalpha),(sinalpha,0,cosalpha),(cosalpha,...
Text Solution
|
If a ,b ,c are in A.P , show that , |{:(x+1,x+2,x+a),(x+2,x+3,x+b),(x+...
Text Solution
|
If A,B,C , are the angles of a triangles, show that, |{:(sin^2A,coaA,1...
Text Solution
|
without expanding prove that [22-24] |{:(7,12,-3),(9,14,-1),(8,13,-2...
Text Solution
|
|{:(1,bc,bc(b+c)),(1,ca,ca(c+a)),(1,ab,ab(a+b)):}|=0
Text Solution
|
|{:(logx xyz,logxy,logxz),(logyxyz,1,logyz),(logzxyz,logzy,1):}|=0
Text Solution
|
if |{:(a+ib,c+id),(-c+id,a-ib):}|xx|{:(alpha-ibeta,gamma-idelta),(-gam...
Text Solution
|
|{:(-a(b^2+c^2-a^2)," "2b^3," "2c^3),(" ...
Text Solution
|
Show that |{:(x-3,x-4,x-alpha),(x-2,x-3,x-beta),(x-1,x-2,x-gamma):}|=0...
Text Solution
|
If a, b, c, are real numbers such that |{:(b+c,c+a,a+b),(c+a,a+b,b+c...
Text Solution
|
Show that , |{:((a^2+b^2)/c," "c," "c),(" "a,(b^2+c^2)/a," "a),(" "b,"...
Text Solution
|
prove that , |{:(1,1+a,1+a+b),(2,3+2a,4+3a+2b),(3,6+3a,10+6a+3b):}|=1
Text Solution
|