Question

The graph of a quadratic polynomial intersects the x-axis at points (-1, 0) and (4, 0). What is the polynomial.

Answer 1

Explanation:

Given:

Graph intersect x-axis at (-1,0) and (4,0)

Roots of the polynomial is (-1,4)

Sum of roots= -1 +4 = 3

Product of roots = -1x4 = -4

Polynomial is $x^{2} -(sum of roots)x - (product of roots)$

= $x^{2} - 3x + 4$

Answer 2

Answer:

The equation of the polynomial is x² -3x -4.

Given:

Given points are (-1,0) and (4,0)

Graph of the polynomial cuts the x - axis.

To Find:

Find the quadratic polynomial.

Step-by-step explanation:

Given points are (-1,0) and (4,0)

As the y coordinates are 0 , therefore they are the roots of the polynomial.

Roots are -1 , 4

α = -1

β = 4

Sum of roots  ,  S = α + β

S = -1 + 4

= 3

Sum of roots  , S  = 3

Product of roots  , P = α.β

P = -1 x 4

= -4

Product of roots  , P = -4

We know equation of quadratic polynomial ,

x² - (sum of roots)x + Product of roots

x² - Sx + P

Putting the values of S and P

x² -3x -4

Hence the equation of the polynomial is x² -3x -4.