Question

if alpha and beta are zeros of polynomial 4x 2 -2x+(k-4) and α=1/β find k

Answer 1

alpha × beta = c / a = (k-4)/4

given that

alpha=1/beta

alpha×beta = 1

(k-4)/4 = 1

k-4 = 4

so k = 8

Answer 2

Answer: k=8

Step-by-step explanation:

• Given Quadratic equation is $4x^{2} -2x+(k-4)=0$ where a=4, b=-2 and c=(k-4).
• We know product of roots $\alpha \beta =\frac{c}{a}$
• Given, $\alpha =\frac{1}{\beta }$

                  ∴ $\alpha \beta =1$

• Now according to question,

        $\frac{c}{a}=1$

    ⇒$\frac{k-4}{4}=1$

    ⇒k-4=4

    ⇒k=4+4

   ∴ k=8

• Hence,the value of k is 8 in the above quadratic equation.

#SPJ2