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  • Are the following statements ‘True’ or ‘False’? Justify your answers. The only value of k for which the quadratic polynomial kx^2 + x + k has equal zeros is .

Are the following statements ‘True’ or ‘False’? Justify your answers. The only value of k for which the quadratic polynomial kx^2 + x + k has equal zeros is .

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Answer.          [False]

 Polynomial : It is an expression of more than two algebraic terms, especially then sum of several terms that contains different powers of the same variable(s).

Quadratic polynomial : when the degree of polynomial is two then the polynomial is called cubic polynomial.

Let p(x)=kx^2 + x + k

Here it is gives that zeroes of p(x) are equal and we know that when any polynomial having equal zeroes then their discriminate will be equal to zero.

i.e. d = 0

b^2 - 4ac = 0            (Q d = b2 – 4ac)

p(x)=kx^2 + x + k

Here, a = k, b = 1, c = k

b^2 - 4ac = 0

(1)2 -4 \times k \times k = 0

1 - 4k^2 = 0

1 = 4k^2

\frac{1 }{4}= k^2

k=\pm \frac{1}{2}

\therefore When +\frac{1}{2}  and -\frac{1}{2}  then the given quadratic polynomial has equal zeroes.

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