You are watching: One of the roots of the equation x^2+kx-6=0 is 3
I understand how you obtained each the the factors, yet do you know that K is -1 since the terms in the factor added together = -1?
And plugging in 3 straight to the equation is one alternate method to solve?
Aug 10, 2019•Comment
David Recine, sirhenryjones-museums.org Tutor
TO address your an initial question, we gain -1 for K by using the FOIL technique to (x-3)*(x+2). This gets us x^2 + 2x - 3x - 6. 2x - 3x = -1x, so yes, the x state in the factor incorporate to do -1.
You"re additionally correct the plugging 3 in because that x and solving because that k will additionally get friend -1:
(x)x + kx - 6 = 0(3)3 + 3k - 6 = 09 + 3k -6 = 03k = 6 - 93k = -3k = -1
Aug 26, 2019•Reply
I resolved by plugging in x=3 in the equation which offers x=-1 therefore c
Jun 24, 2016•Comment
Cydney Seigerman, sirhenryjones-museums.org Tutor
Hi Abhinav :)
I think you expected to compose that when you plugged in x = 3, you discovered k = -1 :) and so quantity A = amount B, which way the answer is C.
Nice job! :)
Jun 25, 2016•Reply
My price was the the relationship have the right to not it is in determined. I plugged in 3 because that x to acquire - 1 because that K, yet then i reasoned that the prompt says that one of the root of the equation is 3, however couldn"t the source be -3 , -2 , or +2 ? Wouldn"t that adjust the value of K once you plug those in?
Aug 12, 2015•Comment
A solitary equation can have an ext than one root - yet that doesn"t change the equation itself. You can think that the roots of an equation together the values of x that will make the equation equal 0.
Here we know that k is -1, therefore the equation is y=x^2-x-6. We know that among the root of the equation is 3, and also if you plug (x=3) right into the equation, climate y=0. The other root is (-2), due to the fact that when (x=-2), y=0. So also though this equation has actually two various roots, the worth of k never changes.
Oct 1, 2015•Reply
In these equations, execute you just assume the +kx is simply the type of the generalized means of writing the equation, so the plus in prior of k is not indicative the the actual authorize of what k is same to? ie x^2 - x - 6.
Nov 3, 2013•Comment
Yes, that"s right. The operation (addition, subtraction, multiplication, etc.) does not denote whether the worth of a change is optimistic or negative. So the equation states " + kx", but if either k or x is a an unfavorable number, the over worth is diminished by that term, due to the fact that we are then adding a an adverse number, i beg your pardon is the very same as subtracting. Does the make sense?
Nov 9, 2013•Reply
Sep 26, 2012•Comment
I to be actually confused by this question due to the fact that it offered the indigenous roots. Isn"t 3 a element of the polynomial no a root?
Aug 27, 2017•Reply
Jonathan , sirhenryjones-museums.org Tutor
Hi,No -- (x - 3) and also (x + 2) are the components of the polynomial.The root of the polynomial are the worths of the variable the make the polynomial same to zero.x = 3 is a root because is renders the polynomial zero.
Sep 4, 2017•Reply
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