Question

9. Sum of zeroes of polynomial P(x) = 4x² – 1 is
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Answer 1

Step-by-step explanation:

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Answer 2

Answer:

Sum of zeros = 0

Note:

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

★ 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 ;

p(x) = 4x² - 1 .

The given quadratic polynomial can be rewritten as ; p(x) = 4x² + 0•x - 1 .

Now,

Comparing with the general form of the quadratic polynomial ax² + bx + c , we have ;

a = 4

b = 0

c = -1

Now,

Sum of zeros = -b/a = -0/4 = 0

Hence,

The required answer is 0 (zero) .

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Also,

If p(x) = 0 , then ;

=> 4x² - 1 = 0

=> 4x² = 1

=> x² = 1/4

=> x = √(1/4)

=> x = ± 1/2

Thus,

The zeros of the given quadratic polynomial are : x = ± 1/2 .

Verification :

Sum of zeros = -1/2 + 1/2 = 0

Also,

-b/a = 0/4 = 0

Hence,

Sum of zeros = -b/a