If f x ,   g x and h x are polynomials of degree 4 and f x g x h x a b c p q r = m x 4 + n x 3 + r x 2 + s x + t be an identity in x ,   then f ''' 0 - f '' 0 g ''' 0 - g '' ( 0 ) h '

Question

If f x , &#160; g x and h x are polynomials of degree 4 and f x g x h x a b c p q r = m x 4 + n x 3 + r x 2 + s x + t be an identity in x , &#160; then f ''' 0 - f '' 0 g ''' 0 - g '' ( 0 ) h ''' 0 - h '' 0 a b c p q r is

Quantrex Academy · Accepted Answer

Correct answer: A. 2 ( 3 n - r )

Given, f x g x h x a b c p q r = m x 4 + n x 3 + r x 2 + s x + t Differentiating both sides with respect to x and determinant along row. &#8658; f ' x g ' x h ' x a b c p q r + f x g x h x 0 0 0 p q r + f x g x h x a b c 0 0 0 = 4 m x 3 + 3 n x 2 + 2 r x + s &#8658; f ' x g ' x h ' x a b c p q r + 0 + 0 = 4 m x 3 + 3 n x 2 + 2 r x + s Differentiating again with respect to x and determinant along row. &#8658; f '' x g '' x h '' x a b c p q r = 12 m x 2 + 6 n x + 2 r &#160; &#160;

If f x ,   g x and h x are polynomials of degree 4 and f x g x h x a b c p q r = m x 4 + n x 3 + r x 2 + s x + t be an identity in x ,   then f ''' 0 - f '' 0 g ''' 0 - g '' ( 0 ) h ''' 0 - h '' 0 a b c p q r is

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If f x , &#160; g x and h x are polynomials of degree 4 and f x g x h x a b c p q r = m x 4 + n x 3 + r x 2 + s x + t be an identity in x , &#160; then f &#39;&#39;&#39; 0 - f &#39;&#39; 0 g &#39;&#39;&#39; 0 - g &#39;&#39; ( 0 ) h &#39;&#39;&#39; 0 - h &#39;&#39; 0 a b c p q r is

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Correct answer

Step-by-step solution

More from Determinants

If f x , g x and h x are polynomials of degree 4 and f x g x h x a b c p q r = m x 4 + n x 3 + r x 2 + s x + t be an identity in x , then f ''' 0 - f '' 0 g ''' 0 - g '' ( 0 ) h ''' 0 - h '' 0 a b c p q r is