Question

 If ∝ and ß are the zeroes of a quadratic polynomial p(x) = x² - 5x + k such that ∝ - ß = 1, find the value of k​

Answer 1

Answer :-

➡ The value of k is 6.

Solving Method :-

 Given Here :- If ∝ and ß are the zeroes of a quadratic polynomial p(x) = x² - 5x + k

Here, ∝ - ß = 1,

To Find :- The value of k

Solving :-

According to the question,

p(x) = x²-5x+k

We haxe ,

• a=1
• b=-5
• c=k

Using the property, α+ β = $\dfrac{-b}{a}$

=$\dfrac{-(-5)}{1}$ = 5

α × β = $\dfrac{c}{a}$ = $\dfrac{k}{a}$ = k

Given here, α - β = 1 in the question,

Squaring both sides, we get,

(α - β)² = 1²

=> α² + β² - 2αβ = 1

=> (α² + β² + 2αβ) - 4αβ = 1

=> (α +β)² -4αβ =1

=> 5² - 4k = 1

=> 25 - 4k = 1

=> -4k= -25+1

=> -4k= -24

=> 4k= 24

=> k = $\cancel{\dfrac{24}{4}}$

=> k=6

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