Question

. If zeroes a and ß of a polynomial X -7X +k are such that a- B =1 then the
value of k.​

Answer 1

$\huge\bf\boxed{\boxed{\underline{\red{Question!!}}}}$

Hello mate your question is wrong ..

okay you're question may be x² - 7x + k

$\huge\bf\boxed{\boxed{\underline{\red{Answer!!}}}}$

Given :

$\huge\mathrm\pink{α \:− \:β = 1}$

To find :

K value

$\huge\mathrm\orange{\:Sum \:of \:zeroes}$

$\mathrm\orange{α - β = \frac{coefficient \:of \:x}{Coefficient \:of \:x²}}$

The equation is x² - 7x + k

let us compare with ax² + bx + c = 0

a = 1 , b = -7 , c = k

$\mathrm\orange{α + β = \frac{-b}{a}}$

$\mathrm\orange{α + β = \frac{-(-7)}{1}}$

$\mathrm\orange{α + β = 7}$

$\huge\mathrm\purple{Product \:of \:zeroes}$

$\mathrm\purple{αβ = \frac{Coefficient}{Coefficient \:of \:x²}}$

$\mathrm\purple{αβ = \frac{c}{a}}$

$\mathrm\purple{αβ = \frac{k}{1}}$

$\mathrm\purple{αβ = k}$

Now substitute the value in the formula :

$\huge\bf\boxed{\boxed{\underline{\blue{(α + β)² - (α - β)² = 4αβ}}}}$

$\mathrm\blue{(7)² - ( 1)² = 4 (k)}$

$\mathrm\blue{49 - 1 = 4k}$

$\mathrm\blue{48 = 4k}$

$\mathrm\blue{\frac{48}{4} = k}$

$\mathrm\blue{k = 12}$

$\huge\bf\boxed{\boxed{\underline{\red{K = 12}}}}$

Now let's find the zeroes :

$\huge\mathrm\green{x² - 7x + 12}$

$\huge\mathrm\green{x² - 3x - 4x + 12}$

$\huge\mathrm\green{x ( x - 3 ) - 4 ( x - 3 )}$

$\huge\mathrm\red{(x-3) (x-4)}$

So if x - 3 and x - 4

So x = 3 and x = 4

$\huge\bf\boxed{\boxed{\underline{\red{Zeroes \:are \:x = 3 \:and \:x = 4}}}}$