Question

find the zeros of 2^x^3 + 5^x^2 - 9x - 18 if it is given that the product of its two zeros is -3​

Answer 1

Step-by-step explanation:

-3. 2. 5 -9. -18

0. -6 3 18

2 -1 -6 | 0

-------

other factors is 2x^2-x-6=0

(x-2)(2x+3)

x=2,x=-3/2

Answer 2

Answer:

Let f( x)= 2x³+5x²-9x-18

Since f(x) is a cubic polynomial, then it must have three zeros.

Let a,b and y are the zeros of f(x).

Then, we get

a×b= (-3). .........I

Now for a cubic polynomial,we know that

Product of the zeros=

-Constant term/coefficient of x³

so, a× b×y= -(-18)/2

a×b×y=9

(-3)×y=9. from EQ.I

y= 9/(-3)

y= (-3)

And sum of the product of zeros taken two at a(-5) time= coefficient of x/coefficient of x³

so,

ab+by+ay= (-9)/2

(-3)+b(-3)+a(-3)= -9/2

-3a-3b= 3-(9/2)

-3(a+b)= -3/2

(a+b)= 1/2. .........2

now by squaring both sides ,we get

(a+b)²= (1/2)²

a²+b²+2ab= 1//4

(a-b)²+2ab+2ab= 1/4. [a²+b²=(a-b)²+2ab]

(a-b)²+4ab= 1/4

(a-b)²+4×(-3)= 1/4

(a-b)²-12 = 1/4

(a-b)²= 12+1/4

(a-b)²=49/4

(a-b)= √49/4

(a-b)= 7/2. ..............3

By adding EQ.s 2 and 3, we get as

(a+b)+(a-b)= 1/2+7/2

2a = 4

so, a=2

By putting a in EQ.i we get

a×b= (-3)

2×b=(-3)

so, b= (-3)/2

Hence ,the zeros of the given polynomial are 2,(-3/2) and (-3).

Hope you will enjoy the solution bestly.