Home
Class 10
MATHS
If ax^(3)+bx+c has a factor of the form ...

If `ax^(3)+bx+c` has a factor of the form `x^(2)+px+1`, show that `a^(2)-c^(2)=ab`.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • POLYNOMIALS

    MTG IIT JEE FOUNDATION|Exercise EXERCISE (Subjective Problems) (Long Answer Type)|4 Videos

  • POLYNOMIALS

    MTG IIT JEE FOUNDATION|Exercise EXERCISE (Subjective Problems) (Integer/Numerical Value Type)|10 Videos

  • POLYNOMIALS

    MTG IIT JEE FOUNDATION|Exercise EXERCISE (Subjective Problems) (Very Short Answer Type )|10 Videos

  • PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

    MTG IIT JEE FOUNDATION|Exercise NCERT SECTION (EXERCISE 3.7)|18 Videos

  • PROBABILITY

    MTG IIT JEE FOUNDATION|Exercise Olympiad/HOTS Corner|26 Videos

Similar Questions

Explore conceptually related problems

If x^(2)+px=1 is a factor of the expression ax^(3)+bx=c, then a^(2)-c^(2)=ab b.a^(2)+c^(2)=-ab c.a^(2)-c^(2)=-ab d.none of these

If x^(2)+px+1 is a factor of the expression ax^(3)+bx+c ,then

If the cubic polynomials x^(3)+ax^(2)+11x+6 and x^(3)+bx^(2)+14x+8 may have a common factor of the form x^(2)+px+q, then (a+p=b+q( b) ap

If x^(2)-1 is a factor of ax^(3)+bx^(2)+cx+d show that a+c=0

If (x^(2)+px+1) is a factor of (ax^(3)+bx+c), then a^(2)+c^(2)=-ab b.a^(2)-c^(2)=-ab c.a^(2)-c^(2)=abd .none of these

If x^(2)-1 is a factor of ax^(4)+bx^(3)+cx^(2)+dx+e, show that a+c+e=b+d

If x^(2)+px+1 is a factor of ax^(3)+bx+c then a a^(2)+c^(2)=-ab b) a^(2)+c^(2)ab c) a^(2)-c^(2)=ab d a^(2)-c^(2)=-ab

If x^(2)-1 is a factor of ax^(4)+bx^(3)+cx2+dx+e, Show that a+c+e=b+d=0