stanslousmubanga817
Answered

Explore Westonci.ca, the premier Q&A site that helps you find precise answers to your questions, no matter the topic. Connect with professionals on our platform to receive accurate answers to your questions quickly and efficiently. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

find the value of k if the roots
of 3x²-5x+k=0, differ by 2​

Sagot :

LammettHash

By the fundamental theorem of algebra, we can write the given quadratic in terms of its roots a and b as

3x ² - 5x + k = 3 (x - a) (x - b)

and upon expanding, we have

3x ² - 5x + k = 3x ² - (a + b) x + ab

Two polynomials are equivalent if their coefficients are equal, so

a + b = 5

ab = k

We're given that |a - b| = 2. If we assume a > b (that is, a is the larger root) then |a - b| = a - b = 2, or b = a - 2. Substitute this for b in the first equation above and solve for a :

a + (a - 2) = 5

2a - 2 = 5

2a = 7

a = 7/2

Solve for b :

b = 7/2 - 2

b = 3/2

Solve for k :

k = 7/2 × 3/2 = 21/4

We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.