Answer:
Step-by-step 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
