stanslousmubanga817
Answered

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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

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