The graph of the polynomial p(x) intersects the x -axis three tim… - Vidyadip

MCQ

The graph of the polynomial $p(x)$ intersects the x -axis three times in distinct points, then which of the following could be an expression for $p(x)$ :

✓
$4-4 x-x^2+x^3$
B
$3 x^2+3 x-3$
C
$3 x+3$
D
$x^2-9$

✓

Answer

Correct option: A.

$4-4 x-x^2+x^3$

(a)
It is given that graph of the polynomial $p(x)$ intersects the $x$-axis three times in distinct points, so the number of zeroes for the polynomial is 3 and it is a third degree polynomial of the form $a x^3+b x^2+c x+d=0$ where $a \neq 0$.
From the given options, the one option matching with the standard equation of a third degree polynomial is $4-4 x-x^2+x^3=x^3-x^2-4 x+4$. Hence, the correct option is (a).

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