If the slope and y intercept of a line are the roots of the equation x^2-7x-18 then the equation of the line can be
Answers
Answer:
9x -y - 2 = 0 or 2x + y - 9 = 0
Step-by-step explanation:
Solution---> ATQ, slope and y intercept of required line is equal to roots of given equation
x² - 7x -18 = 0
Now we find roots of given equation by splitting the middle term method
=> x² - ( 9 - 2 ) x - 18 = 0
=> x² - 9x + 2x - 18 = 0
=> x ( x - 9 ) + 2 ( x - 9 ) = 0
=> ( x - 9 ) ( x + 2 ) = 0
If x - 9 = 0
=> x = 9
If x + 2 = 0
=> x = - 2
So roots are 9 and - 2 .
Now , if , slope of line = 9
length of y intercept of line = - 2
Equation of line in slope - intercept form is
y = mx + c
Where m = slope of intercept , c = length of intercept on y axis
=> y = 9x + ( -2 )
=> y = 9x - 2
=> 9x - y - 2 = 0
If , slope of line = - 2
length of intercept on y axis = 9
Required equation of line
y = mx + c
=> y = (-2)x + 9
=> y = - 2x + 9
=> 2x + y - 9 = 0