Question

If the sum of the zeroes of given polynomial f(x) = ax2 + 2x + 3a is equal to their product, find the value of a.
If a and p are zeroes of a given polynomial f(x)=x²-p(x+2)-c, then find the value of (a+2)(B+2)​

Answer 1

Soln 1:-

Given: f(x) = ax² + 2x + 3a

Sum of zeroes = -b/a = -2/a

Product of zeroes = c/a = 3a/a = 3

ATQ, -2/a = 3

∴ a = -2/3

Hence, the required value of "a" is -2/3.

Soln 2 :-

Given: f(x) = x² - p(x + 2) - c

➟ x² - px - 2p - c

Compare it with ax² + bx + c = 0

➟ a = 1, b = -p, c = -2p-c

Now, α and β are the two zeroes.

✪ Sum of the zeroes = -b/a

α+β = -(-p)/1 = p

✪ Product of the zeroes = c/a

αβ = -2p-c/1 = -2p-c

Now, (α+2)(β+2)

➟ αβ + 2(α+β) + 4

➟ -2p - c + 2(p) + 4

➟ -c + 4

Hence, the value of (α+2)(β+2) is -c + 4.

Answer 2

Answer:

Answers in attachment.

Step-by-step explanation: