Question

5. Find the zeroes of polynomial 2x^2 + 5x - 12 and verify the relationship between its zeroes and its coefficients.

Answer 1

Answer:

x = -4 , 3/2

Note:

• The possible values of variables for which the polynomial becomes zero are called its zeros.

• To find the zeros of a polynomial , equate it to zero.

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

Sum of zeros , (A+B) = -b/a

Product of zeros , A•B = c/a

Solution:

The given quadratic polynomial is :

2x² + 5x - 12 .

Clearly,

a = 2

b = 5

c = -12

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

Thus,

=> 2x² + 5x - 12 = 0

=> 2x² + 8x - 3x - 12 = 0

=> 2x(x + 4) - 3(x + 4) = 0

=> (x + 4)(2x - 3) = 0

=> x = - 4 , 3/2

Now,

Sum of zeros = - 4 + 3/2 = (-8 + 3)/2 = -5/2

-b/a = - 5/2

Clearly,

Sum of zeros = -b/a

Also,

Product of zeros = -4•3/2 = -12/2 = -6

c/a = -12/2 = -6

Clearly,

Product of zeros = c/a

Hence verified.