Question

Show that p(x)=x²-3x²+2x-6 has only one real zero.​

Answer 1

Answer:

How do you show that P(x) = x3 -3x2 +2x -6 has only one real zero?

P(x)=x3−3x2+2x−6,P(3)=33−3(3)2+2(3)−6=0

So x−3 is a factor and x=3 is a zero of above polynomial.

So, P(x)=(x−3)(x2+ax+b)=x3+(a−3)x2+(b−3a)x−3b

Comparing coefficient of x2,

a−3=−3,(a=0)

Comparing coefficient of x0,

−3b=−6,(b=2)

P(x)=(x−3)(x2+2)=0

x=3,±i2–√

So given polynomial has only one real zero x=3.

I hope it is helpful for you.