Question

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What is the minimum value for g(x)=x2−18x+79?

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Answer 1

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P(X) = X²-18 + 79


This equation is in the form of AX²+BX+C = 0

Where,


A = 1 , B = -18 and C = 79



D = B²-4AC


=> (-18)² - 4 × 1 × 79


=> 324 - 316



=> 8

Discriminant Is greater than 0.


So,

The given equation has real unequal roots.


Now,

Solving X²-18X + 79 by Quadratic formula , we have


X = -B (+-) ✓D/ 2A


X = -(-18) (+-) ✓ 8 / 2 × 1



X = 18 (+-) ✓8 / 2


X = 18 (+-) ✓ 2 × 2 × 2 / 2


X = 18 (+-) 2✓2/2


X = 2(9 (+-) ✓2)/2


X = 9 (+-) ✓2


So, ( 9+✓2) and (9-✓2) are the roots of the given equation.



HOPE IT WILL HELP YOU........ :-)