Home
Class 12
MATHS
If f(x) is a polynomial of degree 4 wi...

If ` f(x) ` is a polynomial of degree 4 with rational coefficients
and touches x - axis at ` (sqrt(2) , 0 )` , then for the equation
` f(x) = 0`,

A

sum of roots is 0

B

sum of roots is `4sqrt2`

C

product of rqots is 4

D

product of roots is -4

Text Solution

Verified by Experts

The correct Answer is:
A, C
Promotional Banner

Similar Questions

Explore conceptually related problems

If f(x) is a polynomial of degree n with rational coefficients and 1 +2 i ,2 - sqrt(3) and 5 are roots of f(x) =0 then the least value of n is

Column I: Equation, Column II: No. of roots x^2tanx=1,x in [0,2pi] , p. 5 2^(cosx)=|sinx|,x in [0,2pi] , q. 2 If f(x) is a polynomial of degree 5 with real coefficients such that f(|x|)=0 has 8 real roots, then the number of roots of f(x)=0. , r. 3 7^(|x|)(|5-|x||)=1 , s. 4

Let f(x) polynomial of degree 5 with leading coefficient unity such that f(1)=5, f(2)=4,f(3)=3,f(4)=2,f(5)=1, then f(6) is equal to

If f(x) is a polynomial of degree <3, then, f(x)/((x−a)(x−b)(x−c))​ is equals to

Let f (x) be a polynomial of degree 5 with leading coefficient unity, such that f (1) =5, f (2) =4, f (3) =3, f (4)=2 and f (5)=1, then : Sum of the roots of f (x) is equal to :

Let f(x) polynomial of degree 5 with leading coefficient unity such that f(1)=5, f(2)=4,f(3)=3,f(4)=2,f(5)=1, then f(6) is equal to (a).0 (b). 24 (c). 120 (d). 720

If f(x) is a polynomial of degree four with leading coefficient one satisfying f(1)=1, f(2)=2,f(3)=3 .then [(f(-1)+f(5))/(f(0)+f(4))]

If f(x)=(x-alpha)^ng(x) and f(alpha)=f'(alpha)=f''(alpha)=f^(n-1)(alpha)=0 where f(x) and g(x) are polynomials. For polynomial f(x) and g(x) with rational cofficients , then answer the following questions (1)If y = f(x) touches the x-axis at only one point, then the point of contact

If f(x)=(x-alpha)^ng(x) and f(alpha)=f'(alpha)=f''(alpha)=f^(n-1)(alpha)=0 where f(x) and g(x) are polynomials. For polynomial f(x) and g(x) with rational cofficients , then answer the following questions (1)If y = f(x) touches the x-axis at only one point, then the point of contact

If f(x)=(x-alpha)^ng(x) and f(alpha)=f'(alpha)=f''(alpha)=f^(n-1)(alpha)=0 where f(x) and g(x) are polynomials. For polynomial f(x) and g(x) with rational cofficients , then answer the following questions (1)If y = f(x) touches the x-axis at only one point, then the point of contact