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If `c ,d` are the roots of the equation `(x-a)(x-b)-k=0` , prove that a, b are roots of the equation `(x-c)(x-d)+k=0.`

A

`(x-c) (x-d) - k = 0`

B

`(x-c) (x-d) + k = 0`

C

`(x-a) (x-c) + k = 0`

D

`(x-b) (x-d) + k = 0`

Text Solution

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The correct Answer is:
B
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OBJECTIVE RD SHARMA ENGLISH-QUADRATIC EXPRESSIONS AND EQUATIONS -Exercise
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  2. Suppose that f(x) is a quadratic expresson positive for all real xdot ...

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  3. If c ,d are the roots of the equation (x-a)(x-b)-k=0 , prove that a, b...

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  4. Show that A.M. of the roots of x^(2) - 2ax + b^(2) = 0 is equal to ...

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  5. If alpha, beta are the roots of the quadratic equation x ^(2)+ px+q=0...

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  6. If the roots of the equation (1)/(x+p) +(1)/(x+q) =1/r are equal in ma...

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  7. If the ratio of the roots of the equation x^(2)+px+q=0 is equal to the...

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  8. Find the value of p for which x+1 is a factor of x^4+(p-3)x^3-(3p-5)x^...

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  9. If x ^(2) -3x+2 is a factor of x ^(4) -px ^(2) +q=0, then p+q=

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  10. If the equations x^2+p x+q=0 and x^2+p^(prime)x+q^(prime)=0 have a com...

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  11. If the expression x^(2) - 11x + a and x^(2) - 14 x + 2a have a common ...

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  12. If a,b,c are in GP, show that the equations ax^(2)+2bx+c=0 and dx^(2)+...

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  13. Fill in the blanks If the quadratic equations x^2+a x+b=0a n dx^2+b x+...

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  14. Find the values of a for which the roots of the equation x^2+a^2=8x+6a...

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  15. If the sum of the roots of the equation (a+1)x^2=(2a+3)x+(3a+4)=0 is -...

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  16. If one root of the equation (k-1)x^(2) - 10x+ 3 = 0 is the reciproca...

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  17. If b1. b2=2(c1+c2) then at least one of the equation x^2+b1x+c1=0 and ...

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  18. Solve |x^2+4x+3|+2x+5=0.

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  19. For a alt=0, determine all real roots of the equation x^2-2a|x-a|-3...

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  20. If 2+sqrt(3)i is a root of the equation x^2+p x+1=0 , then write the v...

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