Question

Find the zeroes of the polynomial and verify the relations between the zeroes and coefficients of the polynomial:
4x²-3x-1=0​

Answer 1

Answer:

4x²-3x-1=0

ax²-bx-c

a=4, b= -3, c= -1

sum= -b/a= -(-3)/4=3/4 __1)

product=c/a= -1/4 __2)

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4x²-3x-1=0 | -4x²= (-4x)(x)

4x²-4x+x-1=0

4x(x-1)+1(x-1)=0

(x-1) (4x+1) =0

x-1=0 , 4x+1=0

x=1 | 4x=-1

| x= -1/4

sum= 1+(-1/4)=3/4 __3)

product=1×(-1/4)= -1/4__4)

From there 1=3 and 2=4.

Hence, verified