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34 votes
34 votes
1) Given that f(x)

2x²-3x - 7, where x ER
a) Show that the equation f(x) = 0 has two real roots.
b) Solve the equation f(x) = 0.
=

User DzikiChrzan
by
2.9k points

1 Answer

18 votes
18 votes

Answer:

Explanation:

1) Given that f(x)= 2x²-3x - 7

a) Show that the equation f(x) = 0 has two real roots.

Calculate the discriminant Δ

f(x) = ax²+bx+c

f(x) = 2x²-3x - 7

Δ= b²-4ac = (-3)²-4·2·(-7) = 9 +56 = 65

Δ =65 is

Δ > 0 so the equation has 2 real distinct roots because the discriminant is not 0 or negative, it is a positive number.

b) Solve the equation f(x) = 0.

x= (-b ±√Δ)/2a

x= (3 ±√65)/2·2

One root is x=(3 + √65)/4, the second root is x=(3 - √65)/4

Solutions are x≈2.77 and x≈ -1.27

User Mark Coleman
by
2.9k points
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