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  • The zeroes of the quadratic polynomial x^2 + kx + k, k 0, (A) cannot both be positive

The zeroes of the quadratic polynomial x^2 + kx + k, k \neq 0,

(A) cannot both be positive

(B) cannot both be negative

(C) are always unequal

(D) are always equal

Answers (1)

Answer.  [A]

Solution. Polynomial : It is an expression of more than two algebraic terms, especially the sum of several terms that contains different powers of the same variable(s) and a quadratic polynomial is polynomial of degree 2.

Here the given quadratic polynomial is x^2 + kx + k

a = 1, b = k, c = k

x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}

x=\frac{-k\pm \sqrt{k^{2}-4k}}{2}

x=\frac{-k\pm \sqrt{k(k-4)}}{2}

k(k - 4) must be grater then 0

Hence the value of k is either less than 0 or greater than 4.

If value of k is less than 0 only one zero is positive.

If value of k is greater than 4 only one zero is positive.

Hence both the zeroes can not be positive.

Posted by

infoexpert21

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