Question

Sum of the roots of a quadratic equation is
thrice (3 times) then product. Find k if equation
is x? - 2kx + k-3=0.​

Answer 1

Answer:

Step-by-step explanation:

-2kx+k-3=0

-kx+k=0+3+2

-kx+k=5

-k+k+x=5

x=5

Answer 2

Answer:

The value of k is 9.

Step-by-step-explanation:

The given quadratic equation is x² - 2kx + ( k - 3 ) = 0.

Comparing with ax² + bx + c = 0, we get,

• a = 1
• b = - 2k
• c = ( k - 3 )

We know that,

$\displaystyle{\pink{\sf\:Sum\:of\:roots\:=\:-\:\dfrac{b}{a}}}$

$\displaystyle{\implies\sf\:Sum\:of\:roots\:=\:-\:\dfrac{-\:2k}{1}}$

$\displaystyle{\implies\sf\:Sum\:of\:roots\:=\:-\:(\:-\:2k\:)}$

$\displaystyle{\implies\blue{\sf\:Sum\:of\:roots\:=\:2k}}$

Now,

$\displaystyle{\pink{\sf\:Product\:of\:roots\:=\:\dfrac{c}{a}}}$

$\displaystyle{\implies\sf\:Product\:of\:roots\:=\:\dfrac{k\:-\:3}{1}}$

$\displaystyle{\implies\green{\sf\:Product\:of\:roots\:=\:k\:-\:3}}$

From the given condition,

$\displaystyle{\sf\:Sum\:of\:roots\:=\:3\:\times\:Product\:of\:roots}$

$\displaystyle{\implies\sf\:2k\:=\:3\:\times\:(\:k\:-\:3\:)}$

$\displaystyle{\implies\sf\:2k\:=\:3k\:-\:9}$

$\displaystyle{\implies\sf\:9\:=\:3k\:-\:2k}$

$\displaystyle{\implies\underline{\boxed{\red{\sf\:k\:=\:9\:}}}}$

∴ The value of k is 9.