Question

if alpha ans beta are zeroes of polynomial x²-3x+k such that alpha = 2 beta​

Answer 1

Question:

If alpha and beta are the zeros of the polynomial $x^{2} -3x+k$ such that $\alpha =2\beta$,then find k.

Answer:

alpha = 2 ( Beta )    ===> 1

Sum of the zeros = -b/a

======>  -3/1 = -3

Product of the zeros = $\frac{c}{a}$

========> k/1 = k

Sum of the zeros = -3

$\alpha +\beta = -3$

By using 1,

$2\beta +\beta = -3$

$3\beta =-3\\\beta =\frac{-3}{3} \\\beta = -1\\\Sub\beta = -1 in 1\\\</em></p><p><em>\So,\we\get\[tex]\alpha =-2$\\\

By knowing the values of alpha and beta, let us find the product of the roots which is k

So, we get k=2