Question

27. Find the value of q so that the equation 2x2 - 3px +5q=0 has one root which
is twice the other.

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Answer 1

Answer:

1.2p or 0.3p

Step-by-step explanation:

$a {x}^{2} + bx + c = 0 \\ \\ has \: roots \\ \\ \alpha = - \frac{b}{a} \\ \\ \beta = \frac{c}{a} \\ \\ given \\ \\ a = 2 \\ b = - 3p \\ c = 5q \\ \\ given \\ \alpha = 2 \beta \\ \\ 2c + b = 0 \\ \\ 10q - 3p = 0 \\ \\ else \\ \\ 2 \alpha = \beta \\ \\ 2b + c = 0 \\ \\ 6p - 5q = 0 \\ \\ q = \frac{6}{5} p \: or \: \frac{3}{10}p$

HOPE IT HELPS

Answer 2

$\huge\boxed{\fcolorbox{white}{pink}{Answer}}$

let a & b are the two roots

A/Q

a = 2b

therefore,.

$\Large\boxed{2x^2+3px+5q}$

◆. sum of the roots are a + b = 3p / 2

◆. product of roots are. ab = 5q / 2

on solving we get,

q = 6 / 5 p , 3 / 10p