Question

Find the zeros of the quadratic polynomial 2x^2+x-10.Also verify the relationship between zeros and coefficients

Answer 1

Step-by-step explanation:

2x^2 +X-10

2x^2-4x+5x-10

2x(x-2)+5(x-2)

(2x+5)(x-2)

zeroes are -5/2 and 2

Answer 2

Zeroes are 2 , - 5/2 for   quadratic polynomial 2x²+x-10 and relationship between zeros and coefficients is verified

Given:

quadratic polynomial 2x²+x-10

To Find:

zeros of the quadratic polynomial  2x²+x-10

verify the relationship between zeros and coefficients

Solution:

Quadratic Polynomial is of form ax² + bx + c  where a≠0

Relationship between zeros and coefficients

Sum of zeroes = - b/a

Product of zeroes = c/a

2x² + x - 10

a = 2 , b = 1 , c = - 10

Sum of zeroes = -1/2

Product of zeroes = =10/2 = -5

2x² + x - 10

Using Middle term split

2x² -4x + 5x - 10

Taking 2x common in first two and 5 in last two

= 2x(x - 2) + 5(x - 2)

= (x - 2)(2x + 5)

To find zero equate each factor with zero

x - 2 = 0 => x = 2

2x + 5 = 0 => x  = -5/2

Zeroes are 2 , - 5/2

Sum of zeroes = 2 - 5/2 = -1/2  

Product of zeroes = 2(-5/2) = -5

Relationship between zeros and coefficients is verified.