show your solutions follow the steps and then answer
Answers
Answer:
17) ( d)
18) (c)
19) (b)
20) ( c)
Step-by-step explanation:
17) f(x) = 3x²-2x+1 has no real solutions
Given function is f(x) =3x²-2x+1
On comparing with ax²+bx+c
a = 3
b = -2
c = 1
b²-4ac = (-2)²-4(3)(1)
=> b²-4ac = 4-12
=> b²-4ac = -8
=> b²-4ac < 0
We know that
If ax²+bx+c has no real solutions then b²-4ac < 0
f(x) = 3x²-2x+1 has no real solutions.
18) k = 3
Given equation is f(t) = t²+kt+3
If k = 3 then f(t) = t²+3t+3
On comparing with ax²+bx+c
a = 1
b = 3
c = 3
b²-4ac = 3²-4(1)(3)
=> b²-4ac = 9-12
=> b²-4ac = -3
=> b²-4ac < 0
We know that
If ax²+bx+c has no real solutions then b²-4ac < 0
19) 36 should be added
Given that x²+12x = 13
=> x²+2(x)(6) = 13
On adding 6² = 36 both sides then
=> x²+2(x)(6)+36 = 13+36
=> (x+6)² = 49
=> x+6 = ±√49
=> x+6 = ±7
=> x = ±7-6
=> x = 7-6 or -7-6
=> x = 1 or -13
The solutions are 1 and -13
20)
4x²+2x-2 ≥ 0 is the Quadratic inequality.
Because it is of the degree 2 and having inequation.