Question

If 3 is a root of the quadratic equations X2 - X + k =0,find the value of p so that the roots of the equation X2+k(2x+k+2)+p =0are equal

Answer 1

Here you go❤

${x}^{2} + k(2x + k + 2) + p = 0 \\ use \: {b}^{2} - 4ac \\ b = 2k \\ a = 1 \\ from \: above \: we \: get \\ c = {k}^{2} + 2k + p \\ also \: x \: = 3 \: is \: the \: root \: of \: {x}^{2} - x + k = 0 \\ from \: here \: we \: get \: the \: value \: of \: k \: = - 6 \\ put \: in \: that \: equation \: we \: get \\ {( - 6)}^{2} + 2( - 6) + p = {( - 6)}^{2} \\ p = 12$

Hope it helps ❤