Tue April 10, 2012 By: Divyadutta Behura

So, any linear polynomial in x will be of the form ax + b, where a and b are constants and a ?0 Please explain Why a is not equal to zero?

Expert Reply
Wed April 11, 2012
Any linear polynomial is of the form ax+b. where a should not be zero. If the value of a becomes zero, then it no longer remains a linear polynomial. In that case, the polynomial becomes 0x+b = b. So, there is no x term in this so the ploynomial is not linear. For the polynomial to be linear, it should have x term, that is why the coefficient of x that is a should not be equal to zero.
The same holds for quadratic and cubic polynomial in which if the coefficient of x square or x cube becomes zero then they no longer remain quadratic or cubic. For them to be called quadratic or cubic they should have the term with x square or x cube. So their coefficient must be non zero.
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