Find the sum and product of roots of under root 3X ^2 _under root 6x_3 = 0

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If x_3 is a common factor of x^2_ x+p=0 and x^2 + X +q=0 then find p:q
Put x=3 in both the equations we get p= -6 and q= -12 then p:q = -6/-12 = 1/2 answer

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2015-01-15T11:04:41+05:30

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✔️3x^2 -✔️6x-3=0 comparing it with ax^2 + bx +c =0 we get a= ✔️3 , b = -✔️6 and c= -3 now sum of roots = -b/a = ✔️6/✔️3 =✔️2 and product of roots = c/a = -3/✔️3 = -✔️3 answer
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2015-01-15T12:19:31+05:30

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So for the quadratic equation ax² + bx + c = 0 

sum of roots , s = -b/a

product of the roots, p = c/a

so for the equation  \sqrt{3}x^2- \sqrt{6}x-3=0

we have a = √3 ,  b = - √6 , c = - 3

so s = √2 

and p = -√3
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