Find the zeros of the polynomial p(X)2x²-3x-5?

Question

Answer

2x^2 - 3x - 5
Apply middle term split
2x^2 - 5x + 2x - 5 = 0
2x^2 + 2x - 5x - 5 = 0
2x ( x + 1) -5 ( x + 1) = 0
( 2x - 5) ( x + 1 ) = 0
2x - 5 = 0
x = 5/ 2
x+ 1 = 0
x = -1

Answer

Answer

Introduction:
In this problem, we are asked to find the zeros of the polynomial p(X) = 2x²-3x-5.

Finding the Zeros:
To find the zeros of a polynomial, we need to find the values of x for which p(x) = 0. In other words, we need to solve the equation 2x²-3x-5 = 0.

Using the Quadratic Formula:
One way to solve this equation is to use the quadratic formula, which states that the roots of the equation ax²+bx+c = 0 are given by the formula x = (-b±√(b²-4ac))/2a.

Applying the Quadratic Formula:
Using this formula, we can find the roots of the equation 2x²-3x-5 = 0 as follows:

x = (-(-3)±√((-3)²-4(2)(-5)))/(2(2))

Simplifying this expression, we get:

x = (3±√49)/4

Therefore, the roots of the equation 2x²-3x-5 = 0 are:

x = (3+√49)/4 = 2

x = (3-√49)/4 = -5/2

Conclusion:
Therefore, the zeros of the polynomial p(X) = 2x²-3x-5 are x = 2 and x = -5/2.

Answer

..zeroes are 5/2 and -1.

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