Question

Find the value of k for which one root of the following equation is 6 times of the other
kx^2 + 14x + 8 = 0


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Answer 1

Answer :

k = 3

Step-by-step explanation :

Given,

• one root of the equation kx² + 14x + 8 = 0 is 6 times of the other

To find,

• the value of k

Solution,

Let one root be "a"

the other root = 6a

 Given is a  quadratic equation,

  kx² + 14x + 8 = 0

where

x² coefficient = k

x coefficient = 14

constant term = 8

we know,

Sum of roots = -(x coefficient)/x² coefficient

a + 6a = -14/k

 7a = -14/k

  a = -14/7k

  a = -2/k

 

Product of roots = constant term/x² coefficient

(a)(6a) = 8/k

 6a² = 8/k

 $\sf 6(\dfrac{-2}{k})^2=\dfrac{8}{k} \\\\ 6(\dfrac{4}{k^2})=\dfrac{8}{k} \\\\ \dfrac{24}{k}=8 \\\\ k=\dfrac{24}{8} \\\\ k=3$

∴ The value of k is 3