Question

h
$5$
solve the problem with your own personal data ​

Answer 1

Given 

px^2-14x+8=0

let  a and b be the roots of the equation

b=6a

sum of roots = -b/a

product of roots = c/a

here a=p , b=-14 , c=8

a+b=14/p

ab=8/p

a+6a=14/p

7a=14/p

a=2/p

a*6a=8/p

6a^2=8/p

3a^2=4/p

3*(2/p)^2=4/p

3*4/p^2=4/p

p=3

Answer 2

p = 3

Here, one root is 6 times the other.

So let the roots be a and 6a.

But, as the coefficient of x² is p, the factors become either (x - a) and (px - 6pa), or (px - pa) and (x - 6a).

The second ones are simple to take. So let me take them as factors.

$(px-pa)(x-6a)=px^2-14x+8 \\ \\ px^2-6pax-pax+6pa^2=px^2-14x+8 \\ \\ px^2-7pax+6pa^2=px^2-14x+8$

Take the coefficients of x from both.

$-7pa=-14 \\ \\ pa=2 \ \ \ \ \ \longrightarrow\ \ \ \ \ (1)$

And take the coefficients of x⁰ from both.

$6pa^2=8 \\ \\ pa^2=\frac{8}{6} \\ \\ pa \times a = \frac{4}{3} \\ \\ 2a=\frac{4}{3} \\ \\ a=\frac{2}{3}$

From (1),

$pa=2 \\ \\ \frac{2}{3}p=2 \\ \\ p=2 \div \frac{2}{3} \\ \\ p=2 \times \frac{3}{2} \\ \\ p=\bold{3}$

So the answer is 3.

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