Question

If and beta are the zeros of the polynomial 4 x square - 2 X + (k-4)and alpha=1/beta ,find the value of k

Answer 1

Answer:

GIVES THAT :–

$4 {x}^{2} - 2x + (k - 4) = 0$

AND ROOTS ARE RECIPROCAL.

$\alpha = \frac{1}{ \beta }$

=》

$\alpha \beta = 1$

WE KNOW THAT —

$\alpha \beta = \frac{k - 4}{4} = 1$

$k - 4 = 4$

$k = 8$

#FOLLOW ME....

Answer 2

Given:

➺A quadratic polynomial, 4x² -2x+(k-4) whose zeroes are α and β.

➺ $\bf{\alpha=\dfrac{1}{\beta}\implies\alpha\beta=1}$

To Find:

• Value of k

Solution:

$\rule{200}{2}$

Things to know before solving question:-

For a quadratic polynomial,

• $\sf{Sum\:of\:Zeroes=\dfrac{Coefficient\:of\:x}{Coefficient\:of\:x^{2}}}$

• $\sf{Product\:of\:Zeroes=\dfrac{Constant\:Term}{Coefficient\:of\:x^{2}}}$

$\rule{200}{2}$

For the given quadratic polynomial p(x)= 4x² -2x+(k-4),

$\sf{Product\:of\:Zeroes=\dfrac{Constant\:Term}{Coefficient\:of\:x^{2}}}$

$\longrightarrow\sf{\alpha\beta =\dfrac{k-4}{4}}$

$\longrightarrow\sf{1=\dfrac{k-4}{4}}$

$\longrightarrow\sf{\dfrac{k-4}{4}=1}$

$\longrightarrow\sf{k-4=4}$

$\longrightarrow\sf{k=4+4}$

$\longrightarrow\sf\pink{k=8}$

Hence, the value of k is 8.