Question

50 mark!!
find the quadratic polynomial, where sum and product of of zeroes are a and 1/a
plzz get me the method...
I'll mark you as the brainiest​

Answer 1

Sum of zeros $(\alpha\:+\beta)$ = a

Product of zeros $(\alpha\beta)$ = $\dfrac{1}{a}$

_______________ [GIVEN]

• We have to find the quadratic equation.

____________________________

» Sum of zeros = $(\alpha\:+\beta)$ = a

» Product of zeros = $\alpha\beta$ = $\dfrac{1}{a}$

We know that..

x² - (Sum of zeros)x + Product of zeros = 0

OR

x² - $(\alpha\:+\beta)$x + $\alpha\beta$ = 0

$\implies$ x² - (a)x + $\dfrac{1}{a}$ = 0

$\implies$ $\dfrac{a {x}^{2} \: - \: {a}^{2}x \: + \: 1}{a}$ = 0

____________________________

ax² - a²x + 1 is the quadratic polynomial.

_____________ [ANSWER]

Answer 2

Answer:

let α,β be the zeroes

α+β=a,αβ=1/a

we know

x^2+(sum of roots )x+(product of roots)=0

x^2-ax+1/a=0

ax^2-a^2x+1=0