Question

solve the equation quadratic polynomial and verify relationship 2^2-x-6​

Answer 1

Answer:

x = 2 , -3/2

Note:

★ The possible values of variable for which the polynomial becomes zero are called its zeros.

★ In order to find the zeros of the polynomial , equate it to zero.

★ A quadratic polynomial can have atmost two zeros.

★ If A and B are the zeros of the quadratic polynomial ax² + bx + c , then ;

• Sum of zeros , (A+B) = -b/a

• Product of zeros , (A•B) = c/a

Solution:

Here,

The given quadratic polynomial is ;

2x² - x - 6 .

Clearly,

a = 2

b = -1

c = -6

Now,

Let's find the zeros of the given quadratic polynomial by equating it to zero .

Thus,

=> 2x² - x - 6 = 0

=> 2x² - 4x + 3x - 6 = 0

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

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

=> x = 2 , -3/2

Now,

Sum of zeros = 2 + (-3/2)

= 2 - 3/2

= (4 - 3)/2

= 1/2

Also,

-b/a = -(-1)/2 = 1/2

Clearly ,

Sum of zeros = -b/a

Now,

Product of zeros = 2×(-3/2)

= -3

Also,

c/a = -6/2 = -3

Clearly,

Product of zeros = c/a

Hence verified.