Question

If 1 and -2 are two zeros of the polynomial (x^3-4x^2-7x+10), find it's third zero.

Answer 1

Answer:

if x=1

(x-1)=0

if x= -2

(x+2)=0

now multiply both the eq.

(x-1)(x+2)=0

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

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

now divide the given polynomial in question by polynomial (x^2+x-2)..........

=x-5

i.e. x^3-4x^2-7x+10 =(x-1)(x+2)(x-5)

(x-1)(x+2)(x-5) = 0

• if (x-1) = 0

then , x=1

• if (x+2) = 0

then, x = -2

• if (x-5) = 0

then, x = 5

..............................Hope it helps you..........................

Answer 2

Answer:--

Here's your answer,_________________________________________

Let f(x) = x3 – 4x2 – 7x + 10  

Since 1 and –2 are the zeroes of f(x), it follows that each one of (x–1) and (x+2) is a factor of f(x).  

Consequently, (x–1) (x+2) = (x2 + x – 2) is a factor of f(x).  

On dividing f(x) by (x2 + x – 2), we get:

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Step-by-step explanation: