If alpha and beta are two zeroes of the quadratic polynomial f(x)= 2x2 - 7x +3, Find the polynomial whose zeroes are 1/alpha and 1/beta.
Share
If alpha and beta are two zeroes of the quadratic polynomial f(x)= 2x2 - 7x +3, Find the polynomial whose zeroes are 1/alpha and 1/beta.
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Polynomial:-
[tex] \red{2 {x}^{2} - 7x + 3}[/tex]
Let its zeroes be Alpha and beta:-
[tex]2 {x}^{2} - 7x + 3 \\ 2 {x}^{2} - 6x - x + 3 \\ (2x - 1)(x - 3) \\ \boxed{ \orange{ \alpha = \frac{1}{2} }}[/tex]
[tex] \boxed{ \blue{ \beta = 3}}[/tex]
Now,
For new polynomial:-
[tex]1st \: zero = \frac{1}{ \alpha } = \frac{1}{ \frac{1}{2} } = > \boxed2[/tex]
[tex]2nd \: zero = \frac{1}{ \beta } = > \boxed{ \frac{1}{3} }[/tex]
New Polynomial:-
[tex] = \bf \green{k(x - 2)(x - \frac{1}{3} ) }\\ = k( {x}^{2} - 2x - \frac{1x}{3} + \frac{2}{3} )[/tex]
[tex] = k(3 {x}^{2} - 6x - x + 2 )\over3 \\ [/tex]
Put k = 3:-
[tex] = > \color{cyan} \boxed{3 {x}^{2} - 7x + 2}[/tex]
[tex] \red{ \mathbb{PLZ \: THANKs}}[/tex]