One no. is smaller than other 4 and product of these two no. is 40 ,then the quadratic equations formed is ?
Answers
Answer:
Solution :
Let x and y be the numbers.
One number is 3 less than another number ⟹ x−y=3
Product is 40 ⟹x∗y=40
x−y=3−(1)
x∗y=40⟹x=40y−(2)
Substituting (2) in (1)
40y−y=3
40−y2=3y
y2+3y−40=0
The above quadratic equation can be solved using the formula -
y=−b±b2−4ac√2a
where a = 1, b=3 and c=-40
∴,y=−3±32−4∗1∗(−40)√2∗1
y=−3±9+160√2
y=−3±132
y=5,−8
If y=5,x=405=8
If y=−8,x=40−8=−5
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Lukas Schmidinger, I have passed some math courses in university.
Answered June 5, 2019
One number is 3 less than another number if their product is 40,what are the numbers?
y=x−3
xy=40
Combining this gives us the quadtric equation:
x2−3x−40=0
Using the quadtric formula ax2+bx+c=0⟹x=−b±b2−4ac√2a
We get −5 and 8 thus y=−8 and 5 .
There are two solutions {−8,−5} and {5,8} .
730 views
B.L. Srivastava, M.Sc.Ph.D. Mathematics, Chhatrapati Shahu Ji Maharaj University
Answered June 5, 2019
Let the two numbers be a, b ,then according to the problem (a + 3) = b and (a·b) = 40 . From these two relations , we get, a·(a + 3) = 40 or a^(2) + 3a - 40 = 0 ==> (a - 5)(a + 8) = 0 ==> a = 5 , -8 which in turn gives b = 8 , - 5 respectively . Thus there are two pairs of such numbers & tthese are (a, b) = (5, 8) and (-8, -5) .
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More Answers Below
One number is 3 less than another number. If the sum of the two numbers is 177, what is each number?
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Federico Tancinco, former Purchasing Manager / Math Analyst
Answered June 5, 2019
answer: (-5, -8) & (5, 8)
Let x = 1st number
x-3 = 2nd number
x(x - 3) = 40 ; expand and combine terms
x^2 - 3x - 40 = 0 ; get the factor
(x - 8)(x + 5) = 0 ; equate to get values of x
x - 8 = 0 ; x + 5 = 0
then: x = {-5, 8}
when x = -5 :
x - 3 = -5 - 3 = -8
when x = 8
x - 3 = 8 - 3 = 5
1.5K views
James Wright, BS Physics & Mathematics, University of Illinois at Chicago (1972)
Answered June 9, 2019
Suppose a = b-3, and b(b-3) = 40, then b^2 - 3b = 40, which, when rearranged, becomes
b^2 - 3b - 40 = 0 or (b-8)(b+5) = 0 so b = +8 or -5
The only value of b that is a possible solution is b = 8, making a = 5. The numbers asked for are 8 and 5.
142 views
Shivani Pandey
Answered June 5, 2019
the answer would be 8 and 5
x-y=3
x*y=40
x=40/y
40/y - y =3
y^2 +3y -40=0
y^2 +8y -5y -40=0
Y-5=0 & Y+8=0
Y=5
X=3
173 viewsView Upvoters
Gerry Hardy
Answered June 5, 2019
8x5= 40
94 views
John Kinsella, Lecturer (2005-present)
Answered June 7, 2019
5 and 8
88 views
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