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Sum of the roots of a quadratic equation...

Sum of the roots of a quadratic equation is double their product. Find k if equation is `x^(2)-4kx+k+3=0`.

Text Solution

Verified by Experts

The correct Answer is:
The value of k is 3.
`x^(2)-4kx+k+3=0`
i.e. `x^(2)-4kx+(k-3)=0`
Here, `a=1,b=-4k,c=k+3`
If `alphaandbeta` are the roots of the equation,
`alpha+beta=2alphabeta" "......` (Given)…. (1)
`alpha+beta=-(b)/(a)=-(-4k)/(1)=4k" "....(2)`
`alphabeta=(c)/(a)=(k+3)/(1)=k+3" "....(3)`
From (1), (2) and (3),
`4k=2(k+3):.4k-2k=6:.2k=6:.k=3`
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