Question

iii) The difference between the root of the
equation x2 - 14x + k = 0) is 6. Find k.​

Answer 1

Answer:

x2 - 14x + k = 0

Step-by-step explanation:

$x^2 - 14x + k = 0$ ....... (i)

Compare equation (i) by ax^2 + bx +c = 0

a = 1,  b= -14, c= k

Let α & β be roots of (i)

According to the given condition,

α - β = 6 ........(1)

also we know that α + β = $\frac{-b}{a}$  $=\frac{-(-14)}{1}$ = 14

α + β = 14 .......(2)

Adding (1) & (2)

2α = 20

α = 10

Substitute α =10 in (1)

10 - β = 6

β = 4

Now we know that;

αβ = $\frac{c}{a}$

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

i.e. 10×4= k

k = 40