Question

At how many points the graph of polynomial f(x) = 3 – 2x - x^2 intersect x-axis

Answer 1

Question

At how many points the graph of polynomial

$\bf \: f(x) = 3 - 2x - {x}^{2}$

intersect the x-axis.

Answer

Let, us write the polynomial f(x) in the standard form of quadratic polynomial

$\bf \: f(x) = - {x}^{2} - 2x + 3$

Comparing f(x) with

$\small{ \bf \: a {x}^{2} + bx + c}$

we will get,

a = -1 ; b = -2 ; c = 3

Now,

finding the discriminant (D)

as we know

$\tt discriminant = {b}^{2} - 4ac$

Putting Values

$\tt discriminant = {( - 2)}^{2} - 4( - 1)(3)$

D = 4 + 12

D = 16

Since,

D > 0

therefore,

polynomial f(x) will have two distinct real roots.

Hence,

graph of f(x) will cut the x-axis at two distinct points.