Answered: Suppose that f(x)=−5x2−10x+6. Find the…

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter1: Equations And Inequalities

Section1.CT: Chapter Test

Problem 21CT: 21. Use the Quadratic Formula to solve 3x25x9=0.

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Question

Suppose that f(x)=−5x2−10x+6.
Find the value of k in the quadratic formula below.

x = -k + \sqrt(b^2 - 4ac) / 2a

a) 10

b) − 10

c) 6

d) − 5

e) 100

Expert Solution

Step 1

$G i v e n f u n c t i o n f (x) - f (x) = - 5 x^{2} - 10 x + 6 T h e a b o v e e q u a t i o n i s a q u a d r a t i c e q u a t i o n o f t h e f o r m - a x^{2} + b x + x = 0 a = - 5, b = - 10, c = 6 F o r m u l a f o r f i n d i n g r o o t s o f e q u a t i o n - x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a} S u b s t i t u t i n g v a l u e s - x = \frac{- (- 10) \pm \sqrt{{(- 10)}^{2} - 4 (- 5) (6)}}{2 (- 5)} C o m p a r i n g t h i s w i t h - x = \frac{- k \pm \sqrt{b^{2} - 4 a c}}{2 a} W e g e t, k = - 10$

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