Question

If the sum of a quadratic equation 3x²+(2k+1)x-(k+5)= 0, is equal to the product of the roots, then
the value of k is
1) 2;
2) 4;
3) 6;
4) 8​

Answer 1

it is showing that I am using rude words so I took screenshot :)

hope it helps

Answer 2

We know that,

If α' and 'β' are two zeroes of polynomial ax² + bx + c, then

$\boxed{\purple{\tt Sum\ of\ the\ zeroes=\frac{-b}{a}}}$

OR

$\boxed{\red{\sf Sum\ of\ the\ zeroes=\frac{-coefficient\ of\ x}{coefficient\ of\ x^{2}}}}$

And

$\boxed{\purple{\tt Product\ of\ the\ zeroes=\frac{c}{a}}}$

OR

$\boxed{\red{\sf Product\ of\ the\ zeroes=\frac{Constant}{coefficient\ of\ x^{2}}}}$

$\large\underline\blue{\bold{Given - }}$

• If the sum of a quadratic equation 3x² + (2k+1)x - (k+5)= 0, is equal to the product of the roots.

$\large\underline\blue{\bold{To \:  Find :-  }}$

• The value of 'k'.

Cᴀʟᴄᴜʟᴀᴛɪᴏɴ :

According to statement,

$\rm :\implies\:Sum\ of\ the\ zeroes \: = \: Product\ of\ the\ zeroes$

$\rm :\implies\:\dfrac{-coefficient\ of\ x}{coefficient\ of\ x^{2}} = \dfrac{Constant}{coefficient\ of\ x^{2}}$

$\rm :\implies\:\dfrac{ - (2k + 1)}{3} = \dfrac{ - (k + 5)}{3}$

$\rm :\implies\: - 2k - 1 = - k - 5$

$\rm :\implies\: \boxed{ \pink{ \bf \: k\: = \tt \:4 }}$