Question

Find the zero of 12x²-7×-1 and verify the relationship between zeros and the coefficients

Answer 1

Correct question:

Find the zeros of the quadratic polynomial 12x² - 7x + 1 and verify the relationship between zeros and the coefficients .

Answer:

x = 1/3 , 1/4

Note:

★ The possible values of the 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 ;

12x² - 7x + 1 .

Clearly,

a = 12

b = -7

c = 1

Now,

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

Thus,

=> 12x² - 7x + 1 = 0

=> 12x² - 4x - 3x + 1 = 0

=> 4x(3x - 1) - (3x - 1) = 0

=> (3x - 1)(4x - 1) = 0

=> x = 1/3 , 1/4

Now,

Sum of zeros = 1/3 + 1/4

= (4 + 3)/12

= 7/12

Also,

-b/a = -(-7)/12 = 7/12

Clearly,

Sum of zeros = -b/a

Now,

Product of zeros = (1/3)•(1/4)

= 1/(3•4)

= 1/12

Also,

c/a = 1/12

Clearly,

Product of zeros = c/a

Hence verified.