Question

in the figure , find the value of p and k.

Answer 1

since -2 is a root,
$3 \times {( - 2)}^{2} + 7 \times ( - 2) + p = 0$
This gives p = 2.
Substituting the value of p and rearranging the second equation,
${x}^{2} + 4kx + ({k}^{2} - k + 2) = 0$
Comparing with standard equation,
$a = 1 \: \: b = 4k \: \: c = {k}^{2} - k + 2$
Since roots of this equation is given equal,
${b}^{2} - 4ac = 0$
${(4k)}^{2} - 4 \times 1 \times ( {k}^{2} - k + 2) = 0$
$3 {k}^{2} + k - 2 = 0$
$k = - 1 \: or \: \frac{2}{3}$