Question

if two zeros of the polynomial 2x^4 + 5x^3 - 13x^2 - 25x + 15 are √5 and -√5 find the other zeros of the polynomial ​

Answer 1

sum of zeroes = -5/2

√5 -√5 + a + b= -5/2

a+ b= -5/2

Product = 15/2

√5(-√5)(a)(b)= 15/2

ab= -15/10 = -3/2

a+ b= -5/2

a= -5/2 - b

ab= -3/2

-5/2 - b)(b)= -3/2

5/2 b + b^2 = 3/2

5b + 2 b^2 = 3

2b^2 + 5b -3=0

2b^2 +6b - b -3= 0

2b( b+3) -( b+3)= 0

(2b -1)( b+3)=0

b= 1/2, -3

ab= -3/2

a= -3/2b

= -3/ 2× 1/2 = -3

a= -3/ 2(-3)

= 1/2

So 2 zeroes are 1/2, -3

Answer 2

SEE BOTH ATTACHMENTS CAREFULLY.

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