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  • If one of the zeroes of a quadratic polynomial of the form x^2+ax + b is the negative of the other, then it (A) has no linear term and the constant term is negative.

If one of the zeroes of a quadratic polynomial of the form x^{}2+ax + b is the negative of the other, then it

(A) has no linear term and the constant term is negative.

(B) has no linear term and the constant term is positive.

(C) can have a linear term but the constant term is negative.

(D) can have a linear term but the constant term is positive.

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+ax + b               …..(1)

a = 1, b = a, c = b

Let x1, x2 are the zeroes of the equation (1)

According to question:

x_2 = - x_1

sum of zeroes = x_2 + x_1=\frac{-b}{a}

         x_1 - x_1=\frac{-b}{a}    ( because x2 = - x1 )

0=\frac{-a}{1}\Rightarrow a=0             ( because b = a , a = 1)

Product of zeroes = (x_1)(x_2) = \frac{c}{a}

         = (x_1)(-x_1) = \frac{c}{a}

              = -x_{1}^{2} =b          ( because c= b, a = 1)

Put value of a and b in (1)

x^{2}+ \left (-x_{1}^{2} \right )

Hence, it has no linear term and the constant term is negative.

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