FINDING ZEROS OF QUADRATIC FUNCTIONS WORKSHEET

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

Answer Key

1) 9 and -1.

2)  -1/2 and 5.

3)  -3 and 4/3.

4)   -7 and 1.

5)  x = 12.

6)   -3 and 3.

7)  -4 and 5.

8) 

• 8 yards < 25 yards, the second kick reaches the maximum height.
• 20 yards < 50 yards, the second kick has covered the maximum length.

9) 

10)

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

Example 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

Problem 1 :

Which are the zeros of p(x) = x² + 3x - 10.

a)  5, -2       b)  -5, 2       c)  -5, -2       d)   none of these

Solution

Problem 2 :

Which are the zeros of p(x) = 6x² - 7x + 12.

a)  5, -2         b)  -5, 2       c)  -5, -2      d)  none of these

Solution

Problem 3 :

Which are the zeros of p(x) = x² + 7x + 12.

a)  4, -3        b)  -4, 3       c)  -4, -3     d)  none of these

Solution

Problem 4 :

If the product of zeros of the polynomial ax² - 6x - 6 is 4, find the value of ‘a’.

Solution

Problem 5 :

If one zero of the polynomial (a² + 9)x² + 13x + 6a is reciprocal of the other. Find the value of a.

Solution

Problem 6 :

Find the zeros of the quadratic polynomial x² + 5x + 6 and verify the relationship between the zeros and coefficients.

Solution

Problem 7 :

Find the zeros of the polynomial

p(x) = √2x² - 3x - 2√2.

Solution

Problem 8 :

If α, β are the zeros of the polynomials

f(x) = x² + 5x + 8

then α + β

a)  5       b)  -5       c)  8      d)  none of these

Solution

Problem 9 :

If α, β are the zeros of the polynomials

f(x) = x² + 5x + 8, then α ∙ β

a)  0      b)  1      c)  -1      d)  none of these

Solution

Problem 10 :

The value of k such that the quadratic polynomial

x² - (k + 6)x + 2(2k + 1)

has the sum of zeroes as half of their product is 

a)  2      b)  3        c)  -5      d)  5

Solution