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Which of the following is quadratic expression for all a\, \epsilon \, R

Option: 1

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


Option: 2

\left ( a^{2}+1 \right )x^{2}+x+3


Option: 3

\left ( a+2 \right )x^{2}+x-3


Option: 4

\left ( 2a-1 \right )x^{2}-x+5a


Answers (1)

best_answer

As we learnt in

Quadratic Expression

f\left ( x \right )= ax^{2}+bx+c, where a\neq 0

Now,

In option (A), for a = 1,-1, coefficient of x2 becomes 0, so it is not a quadratic equation for all real values of a.

In option (C), for a = -2, coefficient of x2 becomes 0, so it is not a quadratic equation for all real values of a.

In option (D), for a = 1/2, coefficient of x2 becomes 0, so it is not a quadratic equation for all real values of a.

But in option (B), the coefficient of x2 will be never zero for any real value of a, so (B) will represent a quadratic equation for all a\; \epsilon \; r

Posted by

Rishabh

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