let the quadratic eq ax^2 +bx + c be such that a,b,c are distinct and each of a,b,c belong to {1,2,3.....n} such that x+1 divides ax^2+ bx +c.If such quad.polynomials are < 99,then max(n)=?a)14 b)15 c)16 d)18 e)none of these

The number of non-negative integer solutions of a + b = c ---> c – 1C1 = c - 1. Therefore, number of solutions when c = 2, 3, 4, .., 15 = 1, 2, 3, 4, ... 14 = 105. Out of these we have to remove solutions where a and b are not distinct. it happens when c is even. The number of cases = 7. Therefore, total solutions = 105 - 7 = 98 and answer is b.if y is an integer such that y>=4 and x=y*y -2y,then largest number that divides x*x-8x=?If you substitute x=y2-2y into x2-8x you will obtain,x2-8x = (y-4)(y-2)(y)(y+2)If y is odd:then x2-8x is divisible by 3If y is even:then it has to be divisible by 2 (4!) = 48

For the equation 4x2 - 2xy - 8x + y + 9 = 0, find the number of positive integral solutions.

Hi Tina,Plese find the solution We want to find number of positive integral solutions for (x,y) 4x2 - 2xy - 8x + y + 9 = 0=>4x2 - 8x + 9 = (2x - 1)y=>y = (4x2 - 8x + 9)/(2x - 1) = (2x -3) + 6/(2x-1).Only two values satisfy. (1,5), (2,3)

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11/01/2019 2:52 pm

Nancyjain

(@nancyjain)

Trusted Member

57 Posts
0 52 5

If a=√(7+4√3), what will be the value of a+1/a?

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11/01/2019 2:57 pm

Nancyjain

(@nancyjain)

Trusted Member

57 Posts
0 52 5

If roots of equation (a^2+b^2)x^2-2b(a+c)x+b^2+c^2=0 are equal then a, b, c are in

A) AP

B) GP

C) HP

D) cannot be determined

TG Team 11/01/2019 5:47 pm

PFA the solution 🙂

49947616 1982477725203182 7318753336151244800 o

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13/01/2019 5:35 pm

Nancyjain

(@nancyjain)

Trusted Member

57 Posts
0 52 5

Solve the inequality

3x^2-7x-6<0

TG Team 13/01/2019 6:16 pm

3x² – 7x – 6 < 0.

3x² – 9x - 2x – 6 < 0.

3x ( 3x -2) -2( x-3) < 0.

( 3x – 2) ( x-3) <0

2/3 3
___+ve____|_____-ve _____|____+ve___

2/3 < x < 3

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09/07/2019 12:42 am

aniket prajapati

(@aniketp)

Reputable Member

298 Posts
0 39 259

(7/2+a)²+(7/2+a+x)²=7²-----(1)
(7/2+a-x)²+a²=(7/2)²-----(2)
Find values of a and x ?

Aditya Dang 22/06/2021 11:04 am

For a=0.9086, x= 1.0286 and a= -1.6627, x= 4.9173

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24/08/2019 4:29 pm

tothepoint

(@tothepoint)

Active Member

11 Posts
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@khatri_me

22nd: 3s+5t=750. First solution will be, s=0, t=150. Now, value of t will go down by 3 (which is coefficent of s) for every next solution. Next solution is s=5, t=147, then next will be, s=10, y=144 and so on. Value of t will vary from 150 to 0, with common difference of 3. Hence number of solutions will be {(150-0)/3} +1=51.
If you want to find out natural solutions, then 51-2=49. We subtract 2 because of (0,150), and (250,0).