Question

Find the minimum value of p(x)=x^2+7x+8​

Answer 1

Answer:

-17/4

Step-by-step explanation:

Given,

polynomial is x² + 7x + 8.

The range of polynomial function is given by,

[-D/4a, ∞) for general form of polynomial ax² + by + c where a > 0 and D is discriminant.

Calculating D:

D = b² - 4ac

D = 7² - 4(1)(8)

D = 49 - 32

D = 17

So range is given by,

=> [-D/4a, ∞)

=> [-17/4(1), ∞)

=> [-17/4, ∞)

Hence the minimum value of polynomial is -17/4.

#More

Range is the set of all the possible output values for a function or a polynomial.

For a polynomial where coefficient of x² is negative (a < 0) then it's range is given by (-∞, -D/4a] where D is discriminant of quadratic equation.

• Discriminant, D = b² - 4ac