kwizNET Subscribers, please login to turn off the Ads!
Email us to get an instant 20% discount on highly effective K-12 Math & English kwizNET Programs!

Online Quiz (Worksheet A B C D)

Questions Per Quiz = 2 4 6 8 10

High School Mathematics
6.7 Problems on Roots

Example:
If one root of x2 - (a+1)x - 21 = 0 is -3, find the value of a.
Solution:
If the roots of ax2 + bx + c = 0 are a and b then,
  • Sum of the roots (a + b) = -b/a = (Coefficient of x / Coefficient of x2).
  • Product of the roots (a * b) = c/a = (constant term / coefficient of x2).
Let the roots of the equation x2 - (a+1)x - 21 = 0 be a and b,
one root is -3, i.e. a = -3
Sum of the roots (a + b) = a + 1
-3 + b = a + 1
Product of the roots (ab) = -21
Given that a = -3,
Therefore, -3b = -21
b = 21/3
b = 7
-3 + 7 = a + 1
a = 4 - 1
a = 3
Directions: Solve the following problems. Also write at least 5 examples of your own.
Q 1: If one root of 2x2 - (16+a)x + 25 = 0 is 5/2 find the value of a.
2
-1
1
-2

Q 2: If one root of 2x2 - (7+a)x - 15 = 0 is 5 find the value of a.
3
5
6
4

Q 3: If one root of 2x2 - (3+a)x + 6 = 0 is 2 find the value of a.
3
5
6
4

Q 4: If one root of x2 - (5+a)x + 24 = 0 is 3 find the value of a.
2
4
5
6

Q 5: If one root of x2 - (7+a)x - 56 = 0 is -8 find the value of a.
-6
-8
8
6

Q 6: If one root of 3x2 - (10+a)x + 10 = 0 is 5 find the value of a.
4
5
6
7

Question 7: This question is available to subscribers only!

Question 8: This question is available to subscribers only!


Subscription to kwizNET Learning System offers the following benefits:

  • Unrestricted access to grade appropriate lessons, quizzes, & printable worksheets
  • Instant scoring of online quizzes
  • Progress tracking and award certificates to keep your student motivated
  • Unlimited practice with auto-generated 'WIZ MATH' quizzes
  • Child-friendly website with no advertisements
  • Choice of Math, English, Science, & Social Studies Curriculums
  • Excellent value for K-12 and ACT, SAT, & TOEFL Test Preparation
  • Get discount offers by sending an email to discounts@kwiznet.com

Quiz Timer