Question

find the value of K for which one root of the equation Kx*2-14x+8 is equal to zero is six times of other

Answer 1

root a+ root b = -b/a
14/k = 7
k=2

Answer 2

Let a and b be the Zero of
p ( x ) = kx² - 14x + 8


a = 6b ..... ( i )

$product \: of \: zeros = \frac{constant \: term}{coefficient \: of \: {x}^{2} }$
$ab = \frac{8}{k}$

$6 {a}^{2} = \frac{8}{k}$

6ka² = 8

$k {a}^{2} = \frac{8}{6}$

$k = \frac{4}{3 {a}^{2} }$
.....( ii )

$sum \: of \: zeros = \frac{ - coefficient \: of \: x}{coefficient \: \: of \: {x}^{2} }$

$a + b = \frac{ 14}{k}$
7a = 14/k

k = 2/a .....( iii )

Equating ( ii ) and ( iii )

$\frac{4}{3 {a}^{2} } = \frac{2}{a}$


4a = 6a²

4a/6a = a

2/3 = a

Putting in ( iii )

K = 2/a

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

k = 3