Question

If a and b are zeroes and the quadratic polynomial f(x) = x² - 4x -12, then the value of 1a+ 1/b - a×b is a 35/3 b -35/3 c32//6 d -32/6​

Answer 1

$\underline{\textbf{Given:}}$

$\textsf{a and b are zeroes of the quadratic polynomial}\;\mathsf{f(x)=x^2-4x-12}$

$\underline{\textbf{To find:}}$

$\textsf{The value of}$

$\mathsf{\dfrac{1}{a}+\dfrac{1}{b}-a\,b}$

$\underline{\textbf{Solution:}}$

$\mathsf{}$

$\mathsf{Consider,}$

$\mathsf{f(x)=x^2-4x-12}$

$\mathsf{Sum\;of\;zeroes=\dfrac{-b}{a}}$

$\mathsf{a+b=\dfrac{-(-4)}{1}}$

$\implies\boxed{\mathsf{a+b=4}}$

$\mathsf{Product\;of\;zeroes=\dfrac{c}{a}}$

$\mathsf{ab=\dfrac{-12}{1}}$

$\implies\boxed{\mathsf{ab=-12}}$

$\mathsf{Now,}$

$\mathsf{\dfrac{1}{a}+\dfrac{1}{b}-a\,b}$

$\mathsf{=\dfrac{a+b}{ab}-a\,b}$

$\mathsf{=\dfrac{4}{-12}-(-12)}$

$\mathsf{=\dfrac{-1}{3}+12}$

$\mathsf{=\dfrac{-1+36}{3}}$

$\mathsf{=\dfrac{35}{3}}$

$\implies\boxed{\mathsf{\dfrac{1}{a}+\dfrac{1}{b}-a\,b=\dfrac{35}{3}}}$

$\underline{\textbf{Answer:}}$

$\mathsf{Option\;(a)\;is\;correct}$

$\underline{\textbf{Find more:}}$

Answer 2

TWO ZEROES ARE = a & b

Given Polynomial = x²-4x-12

so,

sum of zeroes = -b/a

a+b = -b/a

a+b = -(-4)/1

a+b = 4

product of zeroes = c/a

a×b = (-12)/1

a×b = -12

NOW, TO FIND

1/a + 1/b - a×b

by taking L.C.M

= b+a/ab - ab

= 4/-12 - (-12) (sum of zeroes =4 & product = -12

= -1/3 +12

(again by taking L.C.M)

= -1+36/3

= 35/3

HENCE THE ANSWER IS 35/3

TANANK U