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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`

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If a >0 and discriminant of a x^2+2b x+c is negative, then Delta = |(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

Prove that: |[a, b, ax+by],[ b, c, bx+cy], [ax+by, bx+cy,0]|=(b^2-a c)(a x^2+2b x y+c y^2)

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If a+b+c=0, one root of [[a-x, c, b],[c, b-x, a],[ b, a, c-x]]=0 is a. x=1 b. x=2 c. x=a^2+b^2+c^2 d. x=0

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If x ^(2)+bx+b is a factor of x ^(3) +2x ^(2) +2x+c (c ne 0), then b-c is :

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If a, b, c ∈ R, a ≠ 0 and the quadratic equation ax^2 + bx + c = 0 has no real root, then show that (a + b + c) c > 0

CENGAGE ENGLISH-DETERMINANTS-All Questions
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  2. Prove that |a ,b+c, a^2,b, c+a, b^2,c, a+b, c^2|=-(a+b+c)xx(a-b)(b-c)...

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  3. If a >0 and discriminant of a x^2+2b x+c is negative, then |[a,b,ax+b]...

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  4. Using the properties of determinants, prove that following |(a-b-c,2a,...

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  5. If a1,a2,a3,.....an.... are in G.P. then the determinant 'Delta=|[loga...

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  6. Using properties of determinants, prove the following |(a^2,ab,ac),(ab...

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  7. Let vec ar=xr hat i+yr hat j+zr hat k ,r=1,2,3 be three mutually perp...

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  8. The number of distinct real roots of |[sinx,cosx,cosx],[cosx,sinx,cosx...

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  9. Let a ,b ,c be real numbers with a^2+b^2+c^2=1. Show that the eq...

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  10. If lines p x+q y+r=0,q x+r y+p=0 and r x+p y+q=0 are concurrent, the...

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  11. If plambda^4+qlambda^3+rlambda^2+slambda+t=|[lambda^2+3lambda, lambda-...

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  12. Find the value of lambdaif2x^2+7x y+3y^2+8x+14 y+lambda=0 represent a ...

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  13. If x ,y ,z are different from zero and "Delta"=|[a, b-y ,c-z],[ a-x, b...

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  14. If A , B ,C are angles of a triangle, then the value of |[e^(2i A),e^(...

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  15. If a^2+b^2+c^2=1, then prove that |[a^2 +(b^2+c^2)cosθ, ab(1−cosθ), ...

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  16. For the equation |[1,x,x^2],[x^2, 1,x],[x,x^2, 1]|=0, There are exa...

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  17. Let Deltar=|[r-1,n,6],[(r-1)^2,2n^2,4n-2],[(r-1)^3,3n^3,3n^2-3n]|. Sho...

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  18. Let m be a positive integer and Deltar=|[2r-1,.^mCr,1],[m^2-1,2^m,m+1]...

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  19. a^(−1)+b^(−1)+c^(−1)=0 such that |[1+a,1,1,],[1,1+b,1,],[1,1,1+c,]| =△...

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  20. Find the area of a triangle whose vertices are A(3,2),B(11 ,8) and C(8...

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