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The value of p if the pair of equations may have one root common is 1.
<h3>What are the roots of the equation?</h3>Let the equation be ax² + bx + c = 0.
Then the roots of the equation will be
The equations are given below.
2x² + px - 1 = 0 and 3x² - 2x - 5 = 0
The roots of the equation 3x² - 2x - 5 = 0 will be
3x² - 5x + 3x - 5 = 0
(3x - 5)(x + 1) = 0
x = -1, 5/3
At x = -1, the value of p will be
2(-1)² + p(-1) - 1 = 0
2 - p - 1 = 0
p = 1
The value of p if the pair of equations may have one root common is 1.
More about the roots of the equation link is given below.
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Recall that the slope-intercept form of the equations of a line is:
Taking both equations to their slope-intercept form we get:
Notice that both equations are the same, therefore the system has infinitely many solutions, therefore it is consistent and dependent.
Answer:
Equations:
The system is consistent and dependent.
A solution to the system is (0,-5).