Question

find the zeroes of the polynomial x2-3x-10 and verify the relationship between the zeroes and the co-efficients

Answer 1

Answer:

hope this answer help you...

And plz mark as brainliest......

Answer 2

Given:

A quadratic equation x² - 3x - 10 =0.

To Find:

The relationship between the zeroes and the coefficients of the quadratic equation.

Solution:

The given problem can be solved using the concepts of quadratic equations.

1. The given quadratic equation is x² - 3x - 10 =0.

2. For finding the zeroes of the given quadratic equation factorization can be used,

=> x² - 3x - 10 =0,

=> x² - 5x +2x - 10 =0,

=>x(x-5) +2 (x - 5) =0,

=> (x-5) (x+2)=0,

=> x = 5, x = -2.

3. Relation between the zeroes and the coefficients:

=> Consider a quadratic equation ax² +bx +c =0, the sum of the roots, and the product of the roots of this quadratic equation is given by the formula,  (-b/a), (c/a) respectively.

=> Verifying the above result with the given equation,

=> Sum of the zeroes = ( 5 - 2 ) = 3 = -(-3/1) = 3. (The result matches with the sum of the zeroes).

=> Product of the zeroes = (5 x -2) = -10 = (-10)/1 = -10. (The result matches with the product of the zeroes).

Therefore, the zeroes of the given polynomial are -2, 5.