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If f(x),g(x) and h(x) are three polynomi...

If `f(x),g(x)` and `h(x)` are three polynomials of degree 2, then prove that `phi(x)` =`|[f(x),g(x),h(x)],[f ^ (prime)(x),g^(prime)(x),h^(prime)(x)],[f^(primeprime)(x),g^(primeprime)(x),h^(primeprime)(x)]|` is a constant polynomial.

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CENGAGE PUBLICATION-DETERMINANTS-All Questions
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  2. Which of the following has/have value equal to zero? |[8, 2, 7],[ 12, ...

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  3. If f(x),g(x) and h(x) are three polynomials of degree 2, then prove th...

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  6. In triangle A B C , if |[1, 1, 1],[cot(A/2),cot(B/2),cot(C/2)],[tan(B/...

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  7. If a ,b ,c ,d ,e, and fare in G.P. then the value of |((a^2),(d^2),x)...

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  8. Prove that: |[(b+c)^2,a^2,a^2],[b^2,(c+a)^2,b^2],[c^2,c^2,(a+b)^2]|=2a...

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  9. If xi=ai bi ci,i=1,2,3 are three-digit positive integer such that ea...

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  10. The system of linear equations x+lambday-z=0, lambdax-y-z=0, x+y-lam...

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  11. If a , b ,c are all different and |[a,a^3,a^4-1],[b,b^3,b^4-1],[c,c^...

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  12. If p q r!=0 and the system of equation (p+a)x+b y+c z=0, a x+(q+b)y+c...

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  13. If c<1 and the system of equations x+y-1=0,2x-y-c=0,a n d -b x+3b y-c=...

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  14. Prove that |x^2x^2-(y-z)^2y z y^2y^2-(z-x)^2z x z^2z^2-(x-y)^2x y|=(...

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  15. If a, b and c are real numbers, and Delta=|[b+c,c+a,a+b],[c+a,a+b,b+c]...

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  16. If a , b , c are non-zero, then the system of equations (alpha+a)x+alp...

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

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

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