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Answers
7. (c) -7
8. (b) 4
9. (c) 13
Sorry buddy I am not able to solve the next
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Answer:
6)(c)
7) (b)
8) (b)
9) (c)
10) (d)
11) (c)
12) (b)
Step-by-step explanation:
6)
All quadratic equations can be solved by the Quadratic Formula.
7)
Given equation is x²-8x+7 = 0
On comparing with the standard quadratic equation ax²+bx+c = 0
a = 1
b = -8
c = 7
We know that
Product of the roots = c/a
=> 7/1
=> 7
8) Given equation is x²-4x-5 = 0
On comparing with the standard quadratic equation ax²+bx+c = 0
a = 1
b = -4
c = -
We know that
Sum of the roots = -b/a
=> -(-4)/1
=> 4
9)
Given number = 169
The square root of 169 = √169
=> √(13)² or √(-13)²
=> ±13
The positive square root is 13
10)
Given equation is x²-30x+c
=> (x)²- 2(x)(15) + c
To get the perfect square we replace c by
15² = 225
=> x²-2(x)(15)+(15)²
=> (x-15)²
11)
Given function is f(x) = (x+2)²-5
=> f(x) = x²+4x+4-5
=> f(x) = x² +4x -1
On comparing with the standard quadratic Polynomial ax²+bx+c
a = 1
b = 4
c = -1
We know that
The axis or line of symmetry of ax²+bx+c is -b/2a
=>x = -4/(2×1)
=>x = -4/2
=> x = -2
Therefore, x = -2
12)
Given that f(x) = (x+2)²+3
=> y = (x+2)²+3
=> y = x²+4x+4+3
=> y = x²+4x+7 -------(1)
on comparing with the standard quadratic Polynomial ax²+bx+c
a = 1
b = 4
c = 7
We know that
Maximum of f(x) occurs f(-b/2a)
=> -4/2(1)
=> -4/2
=> -2
Put x = -2 in (1) then y = (-2)²+4(-2)+7
=> y = 4-8+7
=> y = 11-8
=> y = 3
Therefore, y = 3