Question

If x=-4 is a root of the equation x^2+2x+4p=0, find the values of k for which the equation x^2+px(1+3k)+7(3+2k)=0 has equal roots.

Answer 1

first of all x=-4 is root of the equation so it will satisfy the equation
do find p by putting ×=-4 in the equation
p is -2
then use D=b^2-4ac=0 and put p=-2 in it
{p(1+3k)}^2-4×1×7(3+2k)
eq will be 9k^2-8k-20=0
after solving k=2,-10/9