Question

fi d the quadratic equation whose roots are(-3,-2)​

Answer 1

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 2

Answer:

x^2-(-5)x+6=0

x^2+5x+6 =0 is your answer

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