Suppose 3/4 is a root of a polynomial equation. what does this tell us about the leading coefficient and the constant term in the equation

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Mathematics

Lilianna

17 October, 00:45

Suppose 3/4 is a root of a polynomial equation. what does this tell us about the leading coefficient and the constant term in the equation

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Rosalind · Answer 1

Nothing new about leading coefficient. Definition says it can't be zero. It can always be made equal to one by dividing through.

Constant term cannot be zero unless a root is zero.

Step-by-step explanation:

x-3/4 = 0 has root 3/4 constant term - 3/4

(x-3/4) (x-b) = 0 has roots 3/4 and b, constant term 3b/4 which is zero only if b is zero.

(x-3/4) (x-b) (x-c) = 0 has roots 3/4, b, c, constant term - 3bc/4 which is zero only if b or c is zero.

Etc ...