Home
Class 11
MATHS
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 and `Delta` = `|( f(x), g(x), h(x)), (f'(x), g'(x), h'(x)), (f''(x), g''(x), h''(x))|` then `Delta(x)` is a polynomial of degree (dashes denote the differentiation).

Promotional Banner

Similar Questions

Explore conceptually related problems

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'(x),g'(x),h'(x)),(f''(x),g''(x),h''(x))| is a constant polynomial.

If f(x) , g(x) and h(x) are polynomials of degree 2 , then : phi (x) = |(f(x),g(x),h(x)),(f'(x),g'(x),h'(x)),(f''(x),g''(x),h''(x))| is a polynomial of degree :

If f(x),g(x)a n dh(x) are three polynomial of degree 2, then prove that "phi(x)=|{:(f(x),g(x),h(x)),(f'(x),g'(x),h'(x)),(f''(x),g''(x),h''(x)):}| is a constant polynomial.

If f(x),g(x)a n dh(x) are three polynomial of degree 2, then prove that phi(x)=|f(x)g(x)h(x)f'(x)g'(x h '(x)f' '(x)g' '(x )h ' '(x)| is:

If f(x),g(x)a n dh(x) are three polynomial of degree 2, then prove that phi(x)=|[f(x)g(x)h(x)];[f'(x)g'(x) h '(x)];[f' '(x)g' '(x )h ' '(x)]| is: constant

If f(x), g(x), h(x) are polynomials of three degree, then phi(x)=|(f'(x),g'(x),h'(x)), (f''(x),g''(x),h''(x)), (f'''(x),g'''(x),h'''(x))| is a polynomial of degree (where f^n (x) represents nth derivative of f(x))

If f(x), g(x), h(x) are polynomials of three degree, then phi(x)=|(f'(x),g'(x),h'(x)), (f''(x),g''(x),h''(x)), (f'''(x),g'''(x),h'''(x))| is a polynomial of degree (where f^n (x) represents nth derivative of f(x))

If f(x),g(x)a n dh(x) are three polynomial of degree 2, then prove that varphi(x)=|f(x)g(x)h(x)f'(x)g'(x h '(x)f' '(x)g' '(x h ' '(x)| is a constant polynomial.

If f(x),g(x) andh (x) are three polynomial of degree 2, then prove that f(x)g(x)h(x)f'(x)g'(xh'(x)f''(x)g''(x)h''(x)| is a constant polynomial.