Question

find the zero of x^3-2x^2-15x and verfiy the relationship between zero and cofficient​

Answer 1

Step-by-step explanation:

p(x)= x³-2x²-15x

since,x³-2x²-15x =0

=> x(x²-2x-15)=0

=> x=0 and x²-2x-15=0

=> x²-5x+3x-15=0

=> x(x-5)+3(x-5)=0

=> (x+3)(x-5)=0

x= -3 and x=5

so zeros are 0,-3 and 5.

suppose, α=0, β= -3 and γ=5.

polynomial is in the form of ax³+bx²+cx+d. so, a=1,b= -2,c= -15 and d=0.

since,relation between coefficients and zeros are α+β+γ= -b/a, αβ+βγ+αγ=c/a and αβγ= -d/a.

so,-b/a= -(-2)/1=2 and α+β+γ=0+ (-3)+5=2

c/a= -15/1= -15 and αβ+βγ+αγ=0×(-3)+(-3)×5+0×5=-15.

-d/a=0/1 and αβγ=(0)×(-3)×(5)=0

Hence, verified the relation between coefficient and zeros.