Question

8.A quadratic polynomial whose sum and product of zeroes are 0 and 5 is
(a) x - 5 (b) x + 5 (c) x + X-5. (d) none of the above.
A quadratic polynomial whose zeroes are 1 and --3 is
​

Answer 1

$\huge{\bold{\underline{Solution-:}}}$

$\bold{Quadratic\ polynomial}$= A polynomial which can be written in the form of ax^2 + bx + c

Sum = $\alpha$ + $\beta$ = 0

$\implies$ $\dfrac{-b}{a}$ = 0

$\implies$ $\boxed{\bold{\dfrac{Coeficient\ of\ x}{Coeficient\ of\ x^2}}}$

$\bold{So\ -b\ =\ 0\ and\ a = 1}$

Product = $\alpha$ × $\beta$ = 5

$\implies$ $\dfrac{c}{a}$ = 5

$\implies$ $\boxed{\bold{\dfrac{Constant\ term}{Coeficient\ of\ x^2}}}$

$\bold{So\ c\ = 5\ and\ a =\ 1}$

$\bold{The\ quadratic\ polynomial\ =\ x^2 + 5 }$

Here the correct option is None of the above

Answer 2

Answer:

Step-by-step explanation:

A quadratic polynomial whose sum and Product of zeroes are 0 and 5 is x^2 + 5.

Thus the correct answer is none of the above.

A quadratic polynomial whose zeroes are 1 and - 3 is

x^2 - (1 + (- 3))x + 1×(- 3)

that is

x^2 + 2x - 3.