Question

If one root of quadretic equation x^2-3x+q is twice the other root find value of q

Answer 1

Answer:

value of q = 2

Step-by-step explanation:

Given quadratic equation x²-3x+q = 0,

Let m,2m are two roots of the equation.

Compare given equation with ax²+bx+c = 0, we get

a = 1 , b = -3 , c = q,

$sum \:of \:the \: roots =\frac{-b}{a}$

$\implies m+ 2m = \frac{-3}{1}$

$\implies 3m=-3$

$\implies m = -1\:---(1)$

$product \:of \:the \: roots =\frac{c}{a}$

$\implies m\times 2m = \frac{q}{1}$

$\implies 2m^{2}=q\:---(2)$

/* Substitute m = -1 in equation (2) ,we get

$\implies 2\times (-1)^{2}=q$

$\implies 2 = q$

Therefore,

value of q = 2

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