ZEROS OF POLYNOMIAL WORKSHEET

Problem 1 :

Find zero of the polynomial p(x) = x + 3.

Solution

Problem 2 :

Find the zeroes of quadratic polynomial x²-5x-6.

Solution

Problem 3 :

If 1 is a zero of the polynomial p(x) = ax² - 3(a-1)x - 1, then find the value of 'a' ?            Solution

Problem 4 :

If the graph of a polynomial intersects the x – axis at only one point, can it be a quadratic polynomial?           Solution

Problem 5 :

What number should be added to the polynomial x²-5x+4, so that 3 is the zero of the polynomial?            Solution

Problem 6 :

If x – 3 and x – 1/3 are both factors of ax² + 5x + b , show that a = b              Solution

Problem 7 :

If y = -1 is a zero of the polynomial q(y) = 4y³ + ky² - y -1, then find the value of k

Solution

Problem 8 :

For what value of m is x³ – 2mx² + 16 divisible by x + 2

Solution

Problem 9 :

If p and q are the zeroes of the quadratic polynomial f(x) = 2x² - 7x + 3, find the value of p + q - pq

Solution

Find the zeroes of quadratic polynomial given below.

Problem 1 :

y = (x - 4)² - 25

Solution

Problem 2 :

y = 2x² - 9x - 5

Solution

Problem 3 :

f(x) = 3x² + 5x - 12

Solution

Problem 4 :

f(x) = (-1/2) (x + 3)² + 8

Solution

Problem 5 :

f(x) = x² - 24x + 144

Solution

Problem 6 :

f(x) = 9x² - 81

Solution

Problem 7 :

f(x) = x² - x - 20

Solution

Problem 8 :

A soccer player kicks a ball downfield. The height of the ball increases until it reaches a maximum height of 8 yards, 20 yards away from the player. A second kick is modeled by

y = x(0.4 − 0.008x)

Which kick travels farther before hitting the ground? Which kick travels higher?

Solution

Problem 9 :

Graph the function. Label the x-intercept(s), vertex, and axis of symmetry.

a)  y = (x + 3)(x − 3)

b)  y = (x + 1)(x − 3)

Solution

Problem 10 :

Write the quadratic function f(x) = x² + x − 12 in intercept form. Graph the function. Label the x-intercepts, y-intercept, vertex, and axis of symmetry.

Solution

Problem 1 :

Write a quadratic equation in standard form with solutions, x = -3 and x = 4. Use integers for a, b and c.

Solution

Problem 2 :

Write a quadratic equation in standard form with solutions, x = 2/3 and x = -5. Use integers for a, b and c.

Solution

Problem 3 :

Write an equation of the parabola in intercept form y = a(x - p)(x - q) that has x- intercepts of 9 and 1 and passes through (0, -18).

A) y = -1/2(x - 9)(x - 1)              B) y = -1/2(x + 9)(x + 1)

C) y = -2(x - 9)(x - 1)                 D) y = -2(x + 9)(x + 1)

Solution

Problem 4 :

Write an equation of the parabola in intercept form y = a(x - p)(x - q) that has x- intercepts of 12 and -6 and passes through (14, 4).

A) y = 1/10(x - 12)(x + 6)      B) y = 1/10(x + 12)(x - 6)

C) y = 10(x - 12)(x + 6)         D) y = 10(x + 12)(x - 6)

Solution

Problem 5 :

Determine the equation of a quadratic function given zeros x = 4 and point (3, 2).

Solution

Problem 6 :

Use the intercepts and a point on the graph below to write the equation of the function.

Solution

Problem 7 :

Use the intercepts and a point on the graph below to write the equation of the function.

Solution

Problem 8 :

The sum and product of zeroes of p(x) = 63x² - 7x - 9 are S and P respectively. Find the value of S and P. Find the value of 27S + 14P

a)  -1    b)  1    c)  2    d)  -2

Solution

Problem 9 :

If one zero of the quadratic polynomial 2x² - 8x - m is 5/2, then find the other zero.

a)  1/2    b)  3/2    c)  -3/2    d)  -1/2

Solution