Question

if alpha and beta are the zeroes of px=kx2-3x+2k and alpha+beta=alphabeta, then find the valie of k

Answer 1

I hope it will help you

Answer 2

Answer:-

$\implies \: \red{\boxed{ k = \frac{3}{2} }}$

Step by step explanation:-

To find :-

Find the value of k,

Used concept :-

Here we used sum of roots and product of roots of a quadratic equation.

Solution :-

According to the question,

$\mathcal{p(x) = k{x}^{2} - 3 x + 2k}$

$\small \: if \: \alpha \: \: and \: \beta \: are \: the \: roots \: of \: equation \:$

We know that,

$\star \boxed{ \small \: sum \: of \: roots = \frac{ - coeff. \: of \:x }{coeff. \: of \: {x}^{2} } } \\ \star \boxed{\small product \: of \: roots \: = \frac{constant \: term}{coeff .\: of \: {x}^{2} } }$

Now ,

$\star \: \alpha + \beta = \frac{ - ( - 3)}{k} = \frac{3}{k} \\ \star \: \alpha \beta = \frac{2k}{k} = 2$

According to the question,

$\implies \: \alpha + \beta = \alpha \beta \\ \\ \implies \: \frac{3}{k} = 2 \\ \\ \implies \green{ \boxed{ \: k = \frac{3}{2} }}$

This is the required solution.