Question

sum of roots quadratic equation is double their product find k if equation is x²-4kx+k+3

Answer 1

Hey

Here is your answer,

Given that,

X^2 - 4kx + k + 3 = 0

Sum of zeroes = -b/a
= 4k / 1

Product of zeroes = c/a
= k+3 / 1

Finding the value of k

Sum of zeroes = double the product of zeroes,
4k / 1 = k+3 / 1
4k = k + 3
4k - k = 3
3k = 3
k = 3/3
k = 1

Hope it helps you!

Answer 2

Given−

Quadratic Equation - x² - 4kx + k + 3 = 0

$\large{\underline{\sf{\red{To \: Find-}}}}$

Value of k.

$\large{\underline{\sf{\red{Solution-}}}}$

Here,

a = 1

b = -4k

c = k + 3

$:\implies\rm{α + β = 2α β } \: .... \: (1) \\ </p><p></p><p>:\implies\rm{α + β = - \frac{b}{a}} \\ </p><p> </p><p> </p><p>:\implies\rm{α + β = - \frac{b}{a}} \\ </p><p> </p><p>:\implies\rm{α + β = - \frac{ - 4k}{1} = 4k} \: ... \: (2) \\ </p><p></p><p>:\implies\rm{αβ = \frac{c}{a} = \frac{k + 3}{1} } \\ </p><p></p><p>:\implies\rm{α β = k + 3 }\: ... \: (3)</p><p>$

From (1), (2) and (3),

$:\implies\rm{4k = 2(k + 3)} \\ </p><p>:\implies\rm{4k - 2k = 6} \\ </p><p>:\implies\rm{2k = 6} \\ </p><p>\boxed{\rm\red{k = 3}} </p><p>$

Hence,

The Value of k is 3.