Question

if one zero of polynomial x²-6x+4 is 3+√5 then write other zero​

Answer 1

$\underline\huge\mathcal{\red{Answer:-}}$

$:\implies$ 3 - √5

Step-by-step explanation:

$\underline\huge\mathcal{\red{Question:-}}$

$:\Rightarrow$ If one zero of polynomial x²-6x+4 is 3+√5; then write other zero.

$\underline\huge\mathtt{\purple{Hint:-}}$

$\hookrightarrow$ Here, we are given one of the zeroes of the respective polynomial.

$\hookrightarrow$ We will use the relationship of the zeroes let's say $\alpha$ and $\beta$ to find the other zero which we are asked to find.

$\underline\mathcal{\red{Heya!}}$ $\underline\mathtt{\blue{ Let's \ do \ it!!}}$

$\underline\huge\mathcal{\red{Solution:-}}$

$\bigstar$ $\pmb{\mathfrak{Given}}$

$\bullet{\leadsto}$ p(x) = ${x}^{2}$ - 6x + 4

$\bullet{\leadsto}$ 3 + √5 is one of the zeroes of p(x)

$\bigstar$ $\pmb{\mathfrak{To \ find:-}}$

$\bullet{\leadsto}$ The other zero

Let the two zeroes be $\alpha$ and $\beta$ respectively.

Now, one zero is 3 + √5 that is $\alpha$ = 3 + √5

Also, we know that;

$\alpha \: + \: \beta = \frac{ - b }{a}$

Here, a = 1; b = -6 and c = 4

Putting the values we have

(3 + √5) + $\beta$ = - ($\frac{-6}{1}$)

3 + √5 + $\beta$ = 6

$\beta$ = 6 - 3 - √5

$\beta$ = 3 - √5

Hence, the required other zero is 3 - √5.

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$\tiny\mathfrak{\red{@MissTranquil}}$