Question

If polynomial is x square - 5 x + K and alpha + beta is equals to 2 alpha beta. Find the value of k

Answer 1

$\huge \mathfrak{solution}$

Given:

$\bold{p(x) = {x}^{2} - 5x + k}$

To find :

•K=?

A\Q .

$\star \: \alpha + \beta = 2 \alpha \beta$

As we know that ,

$\alpha + \beta = - ( \frac{b}{a} ) \\ \bold{and} \\ \alpha \beta = \frac{c}{a}$

Here :

a = 1 , b= -5 and c= k

$\rightarrow \: \alpha + \beta = 2 \alpha \beta \\ \\ \rightarrow \: - ( \frac{ - 5}{1} ) = 2( \frac{k}{1} ) \\ \\ \rightarrow \: 5 = 2k \\ \\ \rightarrow \: k = \frac{5}{2}$

Hence the value of k is 5/2

Answer 2

GIVEN:-

• p(x)= x² - 5x +k

• α +β = 2 α×β

SOLUTION:-

➥ p(x)= x² - 5x +k

➥ here, • a = 1 , • b = -5 , • c = k

➥ sum of zeroes = -b/a

➥ .°. α +β = -(-5 / 1)

➥product of zeroes = c / a

➥ .°. 2α×β = 2( K / 1)

➥ sum of zeroes = product of zeroes

➥ .°. α +β = 2α×β

➥ -( -5/1) = 2(k/1)

➥ .°. 5 = 2k

➥ .°. k = 5/2

SO, the value of K is 5/2.