Question

77. If both (x + 2) and (2x + 1) are factors of
axsquare
+ 2 x + b, prove that a - b = 0.​

Answer 1

Step-by-step explanation:( zeros of polynomial: the values of variable at with the polynomial becomes zero).

( when x+a is a factor of polynomial,then x= -a will be it's zero)

{ when a polynomial is divided by it's factor ( say x+a ) then it's remainder is zero . or according to remainder theorem, at x= -a ,the remainder is zero}

we have the given polynomial as;

ax2 + 2x + b

it is given that (x +2) and (2x+1) are the factors of the polynomial,

thus ,x+2 =0 and. 2x +1= 0 ,will be it's zeros.

ie. x= -2 and x= -1/2 are it's zeros.

now ,we know that ,

product of zeros of a polynomial

= constant term/ coefficient of x^2

here,.

=> (-2)(-1/2)= b/a

=> 1= b/ a

=> a=b

hence proved.

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