fi d the quadratic equation whose roots are(-3,-2)
Answers
Answer:
x²+5x+6=0
Step-by-step explanation:
there are actually two ways to solve this. I will show you both.
first if alpha and beta are the two roots we know that
alpha+beta=-b/a
and alpha.beta=c/a
assume that a is 1
i.e -3-2=-b
therefore b=5
and -3.-2=6=c
put a=1 b=5 and c=6
in the general form ax²+bx+c=0
so we get x²+5x+6=0
second one is easier but you will have to memorize a little generalization.
i.e x²-(alpha+beta)x+alpha.beta=0
so x²-(-5)x+6=0
x²+5x+6=0
why there is a minus there I don't know so I prefer to know the concept behind the first method and solve it just using the generalization given above.
you can actually check why alpha+beta and alpha.beta have the values that they have by using quadratic formula and then multiplying and adding the two roots.
(-b+✓b²-4ac)/2a+(-b-√b²-4ac)/2a=-b/a(you can check)
and
(-b+✓b²-4ac)/2a.(-b-√b²-4ac)/2a=c/a (you can check)
Answer:
x^2-(-5)x+6=0
x^2+5x+6 =0 is your answer
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