Question

If a and b are the zeroes of a quadratic polynomial x2 - 5x + b and a-b = 1 then the value of b is

Answer 1

Answer:

hey mate...

a =3,b =2

hope this will help you and you mark me as brainlist ......

Answer 2

Correct Question:

If a and b are the zeroes of a quadratic polynomial (x² - 5x + k) and (a - b) = 1 then the value of k is

$\rule{100}{2}$

Answer:

Here we Have Polynomial : x² – 5x + k

where, A = 1,⠀B = – 5,⠀C = k

$\underline{\bigstar\:\textsf{Relation b/w zeroes and coefficient :}}$

$\qquad\underline{\bf{\dag}\:\:\textsf{Sum of Zeroes :}}\\\dashrightarrow\tt\:\:(a + b) = \dfrac{- \:B}{A}\\\\\\\dashrightarrow\tt\:\: (a + b) = \dfrac{ -\:( - 5)}{1}\\\\\\\dashrightarrow\:\:\underline{\boxed{\red{\tt (a + b) =5}}} \\\\\\\qquad\underline{\bf{\dag}\:\:\textsf{Product of Zeroes :}}\\\\\dashrightarrow\tt\:\: ab = \dfrac{C}{A}\\\\\\\dashrightarrow\tt\:\: ab = \dfrac{k}{1}\\\\\\\dashrightarrow\:\:\underline{\boxed{ \red{\tt ab = k}}}$

$\rule{160}{1}$

$\underline{\bigstar\:\textsf{By the Formula :}}$

$:\implies\tt (a+b)^2-(a-b)^2=4ab\\\\{\scriptsize\qquad\bf{\dag}\:\:\textsf{Putting values :}}\\\\:\implies\tt (5)^2-(1)^2=4k\\\\\\:\implies\tt 25-1=4k\\\\\\:\implies\tt 24=4k\\\\\\:\implies\tt \dfrac{24}{4}=k\\\\\\:\implies\underline{\boxed{\textsf{\textbf{k = 6}}}}$