Question

If alpha,beta are the zeroes of the polynomial f(x)= x square + 5x + 8, then alpha × Beta

Answer 1

Step-by-step explanation:

Given alpha and beta are zeros of p(x)

We know alpha beta form of quadratic polynomial

p(x) = x^2 - (alpha + beta) x + alpha *beta

compare this form with given polynomial

f(x) = x^2 + 5x+8 then

alpha*beta = 8 is the ans.

Answer 2

GiveN :

• Equation is x² + 5x + 8
• α and β are the zeroes

To FinD :

• Value of αβ

SolutioN :

First, see the given equation x² + 5x + 8

And, the as we know that the general form of quadratic equation is ax² + bx + c

Compare both the equations after comparison we get,

a = 1

b = 5

c = 8

As we know that for the Product of Zeros :

✯ Product of zeros = c/a

Put value of zeros,

⇒αβ = 8/1

$\therefore$ Product of Zeros is 8

$\rule{150}{0.5}$

Now, similarly we will find the sum of the zeroes :

✯ Sum = -b/a

⇒Sum = -5/1

⇒ α + β = -5

$\therefore$ Sum of Zeros is -5

______________________

As, we know that the form of equation is :

⇒x² - (sum of zeros)x + Product

⇒x² - (α + β)x + αβ

⇒x² - (-5)x + 8

⇒x² + 5x + 8

So, the sum and product of zeros are verified as same equation is coming