Question

If alpha and beta are the zeros of polynomial 2x2+x-6 ,then form a quadratic equation whose zeros are 1/2alpha and 1/2beta

Answer 1

Answer:

see first find roots from given quadratic polynomial , 2x^2+x-6 =0

=>2x^2 +4x-3x-6=0

=>2x(x-2)+3(x-2)=0

(2x+3)(x-2)=0

x=2/3or ,x=2

These values are given zeroes of quadratic polynomial-->

1/2alpha ,1/2beta

substitute=

1/2(2/3)=1/3

1/2(2)=1/4

formula is-->

x²-(alpha+beta)x+alpha*beta=0

therefore,

x²-(1/3+1/4)x+1/3*1/4=0

ANSWER - - - >>

x^2 - (7/12)x+(1/12)=0

12x^2 - 7x+1= 0

Answer 2

Answer:

Quadratic Polynomial , 2x² + x - 6 = 0

=> 2x² + 4x - 3x - 6 = 0

=> 2x² (x-2) +3(x-2) = 0

=> (2x + 3) (x-2) = 0

x = 2/3 , x = 2

Zeros of Quadratic Polynomial-

- 1/2alpha

- 1/2beta

After Substituting ,,

1/2 (2/3) = 1/3

1/2(2) = 1/4

Formula:

x² - (alpha + beta)x + alpha× beta = 0

Hence,

x² - (1/3+1/4)x + 1/3×1/4 = 0

Thus,

x² - (7/12)x + (1/12) = 0

12x² - 7x + 1 = 0