Question

if alpha and beta are the zeroes of the polynomial f(x)= x²-7x+k such that ( alpha-beta) =1 find the value of k
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Answer 1

Answer:

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Answer 2

$\huge\mathfrak\red{Answer:}$

Given:

• We have been given a quadratic polynomial x² - 7x + k.
• It is also given that α and β are two zeroes of this polynomial such that α - β = 1.

To Find:

• We need to find the value of k.

Solution:

Given f(x) = x² - 7x + k

Sum of zeroes(α + β) = -b/a = -(-7)/1 = 7

Product of zeroes(αβ) = c/a = k/1 = k

Now, inorder to find the value of k, we have

(α - β)² = (α + β)² - 4αβ

Substituting the values, we have

(1)² = (7)² - 4k

=> (1)² = 49 - 4k

=> 1 = 49 - 4k

=> 1 - 49 = -4k

=> -48 = -4k

=> -12 = -k

=> k = 12

Hence, the value of k is 12.