(Q4)Find the zeros of the given polynomials

(i)p(x)=3x (ii)p(x)=x2+5x+6 (iii)p(x)=(x+2)(x+3) (iv)p(x)=x4 - 16

Answer:

(i)Given p(x)=3x

(ii)let p(x)=0

so,3x=0

x=

Zeros of the p(x)=

(ii)Given p(x)=x2+5x+6 is a quadratic polynomial.

It has almost two zeros

to find the zeros,let p(x)=0

x2+5x+6=0

x2+x + x+6=0

x(x+) + (x+)=0

x+=0 or x+=0

x=or x=

therefore the zeros of the polynomial are and

(iii)given p(x)=(x+2)(x+3)

It is a quadratic polynomial.

It has almost two zeros

let p(x)=0

(x+2)(x+3)=0

x+2=0 or x+3=0

x=or x=

therefore the zeros of the polynomial are And

(iv)Given p(x)=x4-16 is a biquadratic polynomial.It has almost two zeros

let p(x)=0

x4-16=0

(x2)2 - 2=0

(x2 - ) (x2 + )=0

(x+) (x-) (x2+)=0

x=(or) x=(or) x2=