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1 answer:
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1) The solution for m² - 5m - 14 = 0 are x=7 and x=-2.
2)The solution for b² - 4b + 4 = 0 is x=2.
<u>Step-by-step explanation</u>:
The general form of quadratic equation is ax²+bx+c = 0
where
- a is the coefficient of x².
- b is the coefficient of x.
- c is the constant term.
<u>To find the roots :</u>
- Sum of the roots = b
- Product of the roots = c
1) The given quadratic equation is m² - 5m - 14 = 0.
From the above equation, it can be determined that b = -5 and c = -14
The roots are -7 and 2.
- Sum of the roots = -7+2 = -5
- Product of the roots = -7
2 = -14
The solution is given by (x-7) (x+2) = 0.
Therefore, the solutions are x=7 and x= -2.
2) The given quadratic equation is b² - 4b + 4 = 0.
From the above equation, it can be determined that b = -4 and c = 4
The roots are -2 and -2.
- Sum of the roots = -2-2 = -4
- Product of the roots = -2
The solution is given by (x-2) (x-2) = 0.
Therefore, the solution is x=2.
Answer: Ian's height = x+14 = 69+14 = 83 cm
Explanation :
Let the height of Jim be x
Let the height of Ian be x+4
Let the height of Lisa be x+4+10=x+14
Since their heights increase by 2cm every months
so after 7 months ,
Jim's height = x+14
Ian's height= x+4+14=x+18
Lisa's height= x+14+14=x+28
According to question,
Sum of Ian's and Jim's height = 170cm
⇒x =
⇒ x= 69cm
∴ Ian's height = x+14 = 69+14 = 83 cm