Find a set of values of k for which the line meets the curve at two distinct points?
Find the set of values of k for which the line y = 2x -k meets the curve y = x^2 + kx - 2 at two distinct points.
Find the set of values of
1 Answer
Sep 13, 2017
Explanation:
"equating the line and the parabola"
rArrx^2+kx-2=2x-k
"rearrange and equate to zero"
x^2+kx-2x-2+k=0
rArrx^2+x(k-2)+(k-2)=0
"with "a=1,b=(k-2),c=(k-2)
"for the equation to have 2 real distinct roots"
"the "color(blue)"discriminant "Delta>0
Delta=b^2-4ac=(k-2)^2-4(k-2)
color(white)(xxxxxxxxx)=k^2-4k+4-4k+8
color(white)(xxxxxxxxx)=k^2-8k+12
"to solve "k^2-8k+12>0" sketch the graph"
"solve "k^2-8k+12=0
rArr(k-6)(k-2)=0rArrk=6,k=2
"coefficient of "k^2>0rArr" minimum " uuu
"consider the parts of the graph above the k-axis"
graph{x^2-8x+12 [-10, 10, -5, 5]}
"solution is "k<2" or "k>6
