Question

Find the value of p if the following pair of equation may have one root common:

Answer 1

The value of p if the pair of equations may have one root common is 1.

What are the roots of the equation?

Let the equation be ax² + bx + c = 0.

Then the roots of the equation will be

$\rm x = \dfrac{-b \pm \sqrt{b^2 - 4 a c }}{2a}$

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.

brainly.com/question/12029673

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