Question

If alpha and bita are zeroes of kx2-2x-3k such that alpha+bita=alpha*bita then k=

Answer 1

Answer:

$-\frac{2}{3}$

Step-by-step explanation:

α, β are the zeroes of $kx^2-2x-3k$

such that α+β=α*β.

$\alpha +\beta =\frac{-3k}{k}=-3$

$\alpha \beta =-\frac{-2}{k} =\frac{2}{k}$

$\frac{2}{k} =-3\\2=-3k\\3k=-2\\k=-\frac{2}{3}$

∴$-\frac{2}{3}$

Relation between Polynomial and Zeroes

There is a quadratic polynomial $ax^2+bx+c$ .(a ≠ 0, two zeroes are α, β)

Then,

$ax^2+bx+c=a(x-\alpha )(x-\beta )=a[x^2-(\alpha +\beta )x+\alpha \beta ]$

∴$\alpha +\beta =-\frac{b}{a}$

∴$\alpha \beta =\frac{c}{a}$

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