4.Form a quadratic equation whose roots are 2 times the roots of the quadratic equation 5x=2x^2-7
@ganeshie8 @Callisto @Jhannybean @zepdrix

Question

anonymous · Answer

$$2x^2-5x-7=0$$

ganeshie8 · Answer

If a number "m" is a root of f(x) then we have f(m) = 0

Notice that the number "2m" is a root of f(x/2) because plugging in x = 2m gives you f(2m/2) = f(m) = 0

ganeshie8 · Answer

so simply replace "x" by "x/2" in the equation to get the equation whose roots are 2 times

anonymous · Answer

how u get $$f( \frac{ x }{ 2 })$$ ?

ganeshie8 · Answer

replace every "x" by "x/2"

anonymous · Answer

okay, i undestand

ganeshie8 · Answer

$$f(x)  = 2x^2-5x-7=0$$

ganeshie8 · Answer

the equation whose roots are 2 times the toots of f(x) would be : 
$$f(\frac{x}{2})~~  =~~~ 2(\frac{x}{2})^2-5(\frac{x}{2})-7=0$$

simplify

ganeshie8 · Answer

2 needs to stay outside the square

anonymous · Answer

okay

michele_laino · Answer

sorry, please, if I call with x_1 and x_2 the roots of your equation, then I can write this:
$$x _{1}+x _{2}=\frac{ 5 }{ 2 }$$
and
$$x _{1}*x _{2}=-\frac{ 7 }{ 2 }$$

anonymous · Answer

$$2(\frac{ x^2 }{ 4 })-\frac{ 5x }{ 2 }-7=0$$ like this? @ganeshie8

michele_laino · Answer

now in serching for an equation whose roots are  2 times x_1 and x_2, I write my new roots as below:
$$z _{1}=2 x _{1},z _{2}=2*x _{2}$$

ganeshie8 · Answer

yes looks good, simplify

anonymous · Answer

okay

anonymous · Answer

$$\frac{ x^2 }{ 2 }-\frac{ 5x }{ 2 }-7=0$$

anonymous · Answer

$$x^2-5x-14=0$$

ganeshie8 · Answer

Perfect !

anonymous · Answer

thnx a lot @ganeshie8  and @Michele_Laino

michele_laino · Answer

Thank you! @MARC_

ganeshie8 · Answer

In general : 
the equation whose roots are "k" times the roots of f(x)=0 is given by f(x/k)=0

anonymous · Answer

okay,thnx again @ganeshie8