Question

The graph of p(x)=3x–2–x² intersects the X-axis in ...... points.Select a proper option (a), (b), (c) or (d) from given options so that the statement becomes correct.
(a) 0
(b) 1
(c) 2
(d) 3

Answer 1

Hi ,

It is given that p( x ) = 3x - 2 - x²

p( x ) = - x² + 3x -2

= - x² + x + 2x - 2

= -x( x - 1 ) + 2( x - 1 )

= ( x - 1 )( - x + 2 )

Two find zeroes of the quadratic

polynomial we have take

p( x ) = 0

( x - 1 )( - x +2) = 0

x - 1 = 0 or - x + 2 = 0

x = 1 or x = 2

p( x ) shows a parabola which intersects

x - axis at two points ( 1 , 0 ) and ( 2 , 0 ).

Options ( b ) and ( c ) are correct .

I hope this helps you.

: )

Answer 2

The zeros of p(x) are the intersections points of the equation, p(x) = 3x – 2 – x² with the x-axis.

∴ The number of distinct zeros of p(x) gives the number of distinct intersection points on the X-axis.
To find the zeros of p(x), consider p(x) = 0
∴3x - 2 - x² = 0
∴ x² - 3x+ 2 = 0
∴ x² - x - 2x+ 2 = 0
∴ x(x - 1 - 2(x - 1) = 0
∴ (x - 1)(x - 2) = 0
∴ x = 1 or x = 2 are the zeros of p(x).
⇒The graph of p(x) intersects X-axis at two points.
The correct options are B and  C.