In the xy-plane, at what two points does the graph of y=(x+a)(x+b) intersect the x-axis?
(1) a+b=-1
(2) the graph intersects the y-axis at (0,-6)
(1) a+b=-1
(2) the graph intersects the y-axis at (0,-6)
y = (x+a)(x+b)
To find the points of intersection with X-axis, substitute y=0,which is the equation of X-axis, in the given equation.
(x+a)(x+b)=0
x = -a or -b.
So, (-a,0) and (-b,0) are the points of intersection on X-axis. (as y-coordinates are obviously zero)
So, the problem is to find a and b values.
statement(1)=> gives only one equation in a and b and hence not sufficient to get a and b
statement(2)=>point of intersection on Y-axis is given (0,-6)
To find the points of intersection on Y-axis, substitute x=0,which is the equation of Y-axis, in the given equation.
y = ab
but the point of intersection is given as (0,-6) => y = -6 = ab
=> this gives a new relation between a and b, which when taken together with statement(1),resolves values of a and b
Answer"C"
