Advertisement Remove all ads

If α And β Are the Zeros of the Quadratic Polynomial F(X) = Ax2 + Bx + C, Then Evaluate α4 + β4 - Mathematics

If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate α4 + β4 

Advertisement Remove all ads

Solution

f(x) = ax2 + bx + c

α + β = `(-b/a)`

αβ = `c/a`

since α + β are the roots (or) zeroes of the given polynomials

then

α4 + β= (α2 + β2)2 -2α2 + β2

= ((α + β)2 - 2αβ)2 - 2(αβ)2

`=[(-b/a)^2-2c/a]^2-[2(c/a)^2]`

`=[(b^2-2ac)/a^2]^2-(2c^2)/a^2`

`=((b^2"2ac")^2-2a^2c^2)/a^4`

  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

RD Sharma Class 10 Maths
Chapter 2 Polynomials
Exercise 2.1 | Q 2.5 | Page 35
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×