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If a in Z and the equation (x-a) (x-10) ...

If `a in Z` and the equation `(x-a) (x-10) +1=0` is integral roots, then the values of a are

A

8,10

B

10,12

C

12,8

D

none

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The correct Answer is:
To solve the equation \((x-a)(x-10) + 1 = 0\) for integral roots, we will follow these steps: ### Step 1: Rearranging the equation We start with the equation: \[ (x-a)(x-10) + 1 = 0 \] Rearranging gives: \[ (x-a)(x-10) = -1 \]
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ML KHANNA-THEORY OF QUADRATIC EQUATIONS -Problem Set - 2
  1. if a lt c lt b, then check the nature of roots of the equation (a ...

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  2. The value of m for which the equation x^(3)-mx^(2)+3x-2=0 has two root...

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  3. If a in Z and the equation (x-a) (x-10) +1=0 is integral roots, then t...

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  4. The equation (6-x)^(4)+(8-x)^(4)=16 has

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  5. If x^(2)+x+1 is a factor of ax^(3)+bx^(2)+cx+d, then the real root of ...

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  6. Let f(x) = ax^(3) + 5x^(2) - bx + 1. If f(x) when divide by 2x + 1 lea...

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  7. If x^3+3x^2-9x=c is of the form (x-alpha)^2(x-beta) , then c is equal ...

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  8. If the two roots of the euqation (lamda-1) (x^(2)+x+1)^(2)-(lamda+1)(x...

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  9. The value of a for which the quadratic equation 3x^(2) + 2a^(2) + 1x...

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  10. If 1 lies between the roots of the equation 3x^(2)-3 sin alpha x -2 co...

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  11. If a.4^(tan x)+ a.4^(-tan x) -2=0 has real solutions, where 0 le x le ...

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  12. If the equation (cos theta - 1) x^(2) + (cos theta ) x + sin theta =0 ...

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  13. If the roots of the equation (x-p) (x-q) =p^(2)- 2q^(2) be real and di...

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  14. The value of a for which the equation 2x^(2)-2(2a+1) x+a(a-1)=0 has ro...

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  15. Find the valuesof m for which exactly one root of the equation x^(2)-2...

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  16. The value of lamda for. Which 2x^(2)-2(2 lamda+1) x+lamda (lamda +1)=0...

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  17. If the equation ax^(2)+bx+c=0 (a gt 0) has two roots alpha and beta su...

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  18. Find the values of a if x^2-2(a-1)x+(2a+1)=0 has positive roots.

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  19. If the equation x^2 +2(a+1)x+9a−5=0 has only negative root, then

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  20. The value of k for which both the roots of the equation 4x^(2)-20kx+(2...

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